OK - compost is not going to "tick off' the horsetail......it's just going to encourage it to grow more vigorously. And 'mulch' is a very generic term - compost can be considered a mulch if applied to the soil surface. Chunky bark mulch doesn't adhere to a slope any better than compost would - it washes off slopes with any good rain. What you want is something that will absorb water and add weight to keep it in place - shredded bark or compost are good for these purposes.

How steep is the slope? You could always use jute netting/geotextiles on a steep bank to assist in stabilization until your groundcover takes over.

I would say somewhere around a 40 degree slope...and everything I've read says that enriching the soil (via compost or other organic matter) will eventually do away with the horsetail (over time) as it thrives in poor soil. That doesn't seem intuitive, but it's what I've read in multiple places. Nothing else seems to be effective so I'm trying it out.

A 40 degree slope will make keeping any mulch material in place difficult unless something is placed to keep it there. The current issue of Fine Gardening magazine has an article about one persons solution to a similar problem with the front yard by placing rocks on that short but steep slope and then amending the soil and planting between the rocks.
Horsetail does grow best in poorer soils and, in my experience, amending the soil with compost can discourage its growth.

I once saw a technique for keeping mulch on a slope: stick small sticks into the ground, not perfectly vertical but tilted slightly uphill, leave them sticking out a couple of inches, then mulch. The sticks hold the mulch pieces from sliding downhill until vegetation takes hold. They don't have to be two inches apart, but closer than two feet. If you have a large area that could be a lot of sticks, but it seems to work and it's essentially invisible.

From a fellow PNW'er and one who has done battle both in my garden and in clients' gardens for years, I can tell you that horsetail just laughs at improved soils. It prefers moist soils but will tolerate quite dry conditions as well and is adaptable to a wide range of pH. Landscape fabric/weed cloth, mulch, even black plastic has minimal effect on discouraging growth.

The ONLY effective control is diligence in removing the top growth, either with herbicides or manual removal. This eventually weakens the root system to the point the plant dies off in that area.