Taxus x media 'Beanpole' is as about as skinny as a conifer can get but even this will exceed a 1' width in time. But far more amenable to pruning than many other conifers.

Taxodium disticum 'Peve Minaret' and you can cut all of the branches off very easily or cut them to 1-2" and have a totem pole. I have a forest of them.

Id like to mention Toskana Smaragd arborvitae i saw while surfing the web, maybe only available in Europe. Its just really nice looking.

There's a couple of yews. There's a couple of a lot of things...finding them is not always so easy. Ames juniper, for instance. Degroot spire arb might be the most widely available narrow accent I know of, still slightly wider and ultimately taller.

Conifers or evergreen? Some Norwood, Graham blandly, see rink, or similar would only need some tying/wrapping to keep shape. Not sure how'd they'd do in your weird climate zone.

Those dimensions only possible with shearing. Also might have to install a frame and keep the plants tied to it as though they were vines, in order to maintain the shape through snowfalls and winds.

The frame would also have to be 10 ft. high, of course. And as with a broader, free standing yet sheared hedge you'd have to be able to shear a 10 ft. tall feature every year.

Notice here how broad the lower part of even this aforementioned initially extra narrow growing form becomes:

http://www.bing.com/images/search?q=de+groot+spire&FORM=HDRSC2

If you're trying to block a view there is probably a smarter way to go about it than erecting a 10 ft. living wall over near the view itself (a recurring question is how to screen a building next door, using plantings installed right in front of the building). A wall that may take 20 years to reach 10 ft. high.

Smarter ways like blinds, curtains, a trellis - over where you are looking from or sitting, instead of near where the view is. The closer you get to the disliked object or scene the bigger the screening has to become.

In addition to sometimes falling open that one is not suitable for shearing in the manner of an arborvitae or yew. And is too tall. For instance one in the Seattle arboretum was over 37 ft. high in 2004-5.

Of the arborvitae cultivars 'Emerald Green' and 'DeGroot's Spire' which one will be narrower at the base ceteris paribus? (I know it will be more than 1')

Probably pretty comparable much of the time. Otherwise shapes assumed by 'Smaragd' (Emerald Green is a translation and not the name of the plant) do vary quite a bit (try a web image search), probably due to positions of propagation material on stock plants as well as final planting site environmental conditions. Similar factors would be likely to affect outcomes with the other selection also.

Degroot spire will be narrower.

Agree with Embo - both are usually quoted at the same mature width (3-4') with the DeGroot's somewhat frequently slightly larger (4-6').

Don't let the "spire" in the cultivar name confuse you:-) Generally a taller and plumper version of arborvitae than is 'Smaragd'.