I'd go with hypericum calycinum or geranium macrorrhizum. Both are great weed suppressors. Consider also phlox subulata.

Juniperus conferta 'Blue Pacific'. Relatively cheap, beautiful and most BB carry them. Pretty good weed suppressor when well-grown and established. Also good at holding soil since they root as they spread.

Since we don't know where you are located, it's hard to make appropriate suggestions :-) As a landscape designer I do a lot of groundcover installations and many of them on slopes.....and weed suppression is always on the top of the list of requirements as slopes are very hard to weed easily. I'd offer these specific characteristics for a good GC for this purpose:

-fully evergreen

-spreads rapidly

-layers on itself to form a dense mat

-requires minimal maintenance to establish

That would rule out the geranium (only semi-evergreen), the juniper (slow to establish and spread; does NOT root as it goes {not a feature offered by any conifer}, prefers a full sun location), and the hypericum is extremely prone to rust, disfiguring the planting and retarding growth). And creeping phlox is subject to significant winter dieback and can look very ratty very fast.

That leave the two you list originally. Of those, the jasmine will accomplish the most the fastest and is really not invasive....just an aggressive spreader :-) Which is exactly what you want!

In my area, an alternate selection would be creeping raspberry, Rubus calycinoides. Spreads rapidly, forms a thick mat, fully evergreen, attractive appearance (bronze winter coloring, great textural foliage, white flowers sometimes followed by edible gold berries). And it is not thorny....stems are just slightly bristly. IME, this is never plagued by any insect or disease issues and is fully winter hardy to z6, tolerates full sun to heavy shade and is very drought tolerant once established.

Creeping raspberry/Taiwan creeper:

" the juniper (slow to establish and spread; does NOT root as it goes {not a feature offered by any conifer}"

Juniperus conferta 'Blue Pacific' most certainly does root as it spreads. I have several plants from such natural propagation to prove it. Also it is a relatively fast spreader. Not like kudzu mind you, but easy and quickly establishes. It can also take some partial shade and look and perform just fine.
Many other groundcover junipers root as they spread. I have 6 new Juniperus horizontalis 'Blue Chip's from natural layering I planted just a week or so ago.

I have a small mound of soil on my property, kind of like on this pic https://en.wikipedia.org/wiki/Zaleski_Mound_Group#/media/File:Ranger_Station_Mound,_southern_side.jpg - that high, but a little smaller.

What kind of ground cover I could use in my climate: South-Central BC, zone 5a, extremely hot during summer, that will fulfill requirements specified by gardengal (preferably evergreen, spreads rapidly, forms a dense mat, requires minimal maintenance) and will grow well on the round slope (S, W, N, and E exposure)? Would Juniperus horizontalis 'Blue Chip' be happy there on all four sides of the mound?

Creeping raspberry may do it but IMO is quite weedy looking and it won't be a good choice if there is clay or other soil that does not drain well. On the other hand, I have quite good experience with hypericum calycinum (rust is not such a big deal where I am) and also creeping phlox doesn't die on me through winter. Both of these are far more appealing to me than creeping raspberry. In the terms of erosion control, english ivy would do a far better job than asiatic jasmine and creeping raspberry.

@windberry, the only possible option for your rather cold winter area that I can recall is thymus praecox (creeping thyme), but you haven't mentioned the soil type. It is an important factor when considering ground covers as well as other plants. Thymus praecox is great when you have well-drained soil and is on the edge of your growing zone and can tolerate foot traffic quite well. Juniper, on the other hand, doesn't grow rapidly. Periwinkle (vinca minor) or creeping phlox (phlox subulata) are some options. It's up to you what you're looking for.

There is not a perfect ground cover especially for zone 5, so you have to decide what's the most valuable feature to you: as low as possible (creeping thyme, periwinkle, creeping phlox), great weed suppressor but not so low (hypericum calycinum, juniper) or not entirely evergreen (geranium macrorrhizum - it's one of the best weed suppressors I know despite being semi-evergreen), fast growth (periwinkle, hypericum calycinum),

http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?taxonid=281446&isprofile=0&

http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=u760

" Would Juniperus horizontalis 'Blue Chip' be happy there on all four sides of the mound?"

I believe it would be tickled to death. It is reputedly hardy to z3. It wouldn't cover your mound in a single season but good things are worth waiting for. The more of them you plant the quicker the coverage.

Also check into Kinnikinnick. You would have to decide if it would be happy in your growing conditions.

Thank you both.

@SeedG: Zone 5 is not that bad as you may think :-) I have quite a few ground covers (Sedums, Sempervivums, 3 kinds of Thyme, Veronica, Ajuga, ornamental Strawberries, Waldsteinia, Iberis, Cerastium, Phlox subulata, Delosperma and some others) growing on my prop, but with none of them, because of varied reasons, I would like to cover my little hill.

Periwinkle? Maybe, but Periwinkle is considered invasive in BC, so it goes out of competition. Hypericum calycinumis looks interesting, but grows too tall. What I have been thinking about more and more often is prostrating Juniperus.

BTW my soil is sandy with what I consider as almost “too good” drainage.

@Kyle “I believe it would be tickled to death.” So you think it could be happy here regardless on which side of the hill it is planted? My main concern is the terrible heat during the summer here, especially on the S and W facing slopes the heat could be unbearable. And how about the N side of the mound, will the Juniper survive and thrive in very bright conditions, but without direct sun?

As for Kinnikinnick, it is native in my area and I have it growing here in part shade. I like it, but I doubt it would like to grow on the slope; too dry, too hot, too much sun exposure.