I went to the local community college while working part-time for my employer in order to get set up with my trade (I was a maintenance electrician, which also included some programming, etc). The route I took was 2 years of the college/work program which got me an associates in engineering technology, and entrance into my employer's apprenticeship program. After I graduated I started working full-time, and spent three years in the apprenticeship program before becoming a journeyman. One issue with the way I did it was that we are not licensed electricians. However, I can still work at many locations throughout the country just fine.
My group was the first to go through this program on a decent scale (previous, it was a trial run of only three people). The oldest person(s?) in my group to make it through to graduation and into the training program was in his/her 40s at the time. The next year had someone who was already in his 50s.
So, yes, it can be done. I've since moved to a new position (still a trade, but no longer maintenance). I have to work a rotating shift now, but honestly it was the best move I could have made. The shift work can be hard for some, but the physical, having to crawl around and get banged up, back breaking work is now much reduced. The most physical job I do now is when I have to turn a valve, and we have nice big equipment for when it is too difficult!
You have to weigh short term sacrifices (always being tired, going to school, studying and working all the time) against the long term benefits (better pay, a job you enjoy, etc).
My job thankfully does not fall into the feast or famine aspects of construction and will hopefully stay secure until I retire at 57. Some people look down on those who work trades, but many of us "worker bees" are still pulling in over $100k/year, have good health benefits, a pension, some sort of match on retirement, etc. A few of the guys I went to school with who went for the "big paying job" (one I don't want, I'm more than happy where I am) are making $55/hour doing a mostly desk job that is still considered a trade (the desk job is the main reason I don't want it--they are stuck in one room their full shift, where as I can go inside, outside, walk around, etc as I please if I'm not actively working a job). And, like me, they only have to work 7 days every two weeks, where anything over that is overtime.