My question is this - will I need a temperature controlled environment for woodworking? If so, what's the most economical way to do so?
I have thought about assembling things inside after they've had a chance to acclimate, but not sure if that would be feasible.
Yes and no. It's ideal to have a space that is comfortable for you to work in, but one with wildly greater temperature swings than you'd accept in your home shouldn't hurt the work
most of the time. Joints could theoretically come apart if you've got a huge temperature/humidity swing, but really, once your material is seasoned you should be fine if you allow more time for the glue to dry. A shop I've worked in could get pretty chilly and nothing ever happened to my pieces. But then, I usually also finished pieces in a few weeks at most and my work-spaces weren't completely unheated. If you leave a piece out in the shop for months/years and the temperature and humidity swings wildly over that period, you might have problems.
For most any kind of finishing (paint, lacquer/clear coat, stain might be ok though), you need a temperature and humidity controlled environment; or at least, need to wait for ideal environmental conditions.