We bought our house this summer and have a 3ft, well established rosemary bush in the garden. It did well this summer and fall, it even bloomed. However we had 2 unusually heavy snows this winter and the plant is brown now. Will it come back?

What zone are you in? The whole thing brown?
Rosemary is a tropical plant that usually wont winter over outside. I'm zone 5 and it wont survive winters here.

I'm in zone 7, but from the size and looks of this plant, I think is has been outside during previous winters, but I may be wrong. I scratched the base of one of the largest branches (about 1 1/2 inch diameter) and it was yellow and moist.

I don't grow Rosemary..so can not say first hand, But what I probable would do is either wait until it warms up more and see if it comes back on its own...Or prune it some, Sage which does over winter well sometimes looks pretty ragged after winter, Most woody type herbs need to be pruned yearly, prune out only the most woody branches and the ends of the others and wait and see what warm weather brings for it. Be sure and post how it turned out later.

Sounds like theres still ome life in it. I'd wait and see if the ends green up. If any branches are brittle I'd prune them off.
I love rosemary. Cant wait to get one for the summer.