You can only prune back to where there is green growth on an Arborvitae. This winter was hard on Arbs from Kansas to Michigan, so many folks feel your pain. Technys are nice plants so, depending on how bad they are, I would try to save them.

tj

Thanks, tj. As I suspected, unfortunately. Will trimming them as much as possible offer any advantage - does it give them a chance to get a 'stronger core' or am I better off simply shaping for looks?

Well, a picture would help, but there are advantages to both approaches. Cutting the most splayed branches back would make them less prone to snow damage, but the more green you cut off, the harder it is on the plant. You never want to cut more than a third off any plant, and conifers may be even more sensitive. With as tough as this winter was on plants, I'd opt for the least amount of trimming this time around.

tj