I spent the past couple of years getting up at 5AM to catch a train to work. If I missed the train, it meant being an hour late for work. A couple of months ago, we moved and I no longer have to get up at 5AM to catch the train, and the consequences of missing my regular public transit to work are much less (my backup option just means being 5-10 minutes late). I still get up at 5AM (to do other stuff), but I'm SO much less tired than I was before. I realized (after the fact) that anxiety about sleeping through my alarm/missing the train was really messing with my sleep cycle--if I woke up in the middle of the night and it was after midnight, I'd have a hard time getting back to sleep because it would be in my head that I had only ____ amount of time left before my alarm went off. Now if I wake up in the middle of the night, I roll over and go back to sleep--I know if I do miss my alarm, it's not a big deal, as I have more wiggle room in the time between waking up and leaving the house.
I'm in bed for the same amount of hours each night now, but when the end of the week comes around, I feel ready to do stuff over the weekend and I actually still wake up sometime between 5-530 on weekends. When I HAD to get up at 5AM, I was exhausted by the end of the week. It was really hard for me to get up before 7, sometimes I even needed to sleep in until 8 or 9 to feel rested. I've never been one to enjoy sleeping in so being unable to easily get up before 8 or 9 was kind of a big deal for me.
Personally, I guess I would probably start paying for gym membership. If the money really bothers you, maybe examine whether or not there are not-so-great health or spending choices going on that are attributable to lack of sleep? For example, do you find yourself relying on convenience foods or restaurants more than you'd like because you are too tired to cook? I've noticed also since I stopped my morning commute craziness that I have more energy for things like taking a quick walk on my lunch break, and I also get fewer cravings for an afternoon pick me up of chocolate, candy, hot cocoa, etc. I always "knew" that being sleep-deprived made me eat more poorly, but I've really had that reinforced recently by seeing how much less I care that there are pastries in the breakroom at 3pm (or whatever) now that I'm properly rested. I guess I'm saying you might want to scrutinize your overall health situation and consider whether or not the lack of sleep is contributing to your need for a gym membership!
Also, I know you say it is too cold to exercise outside for 6 months of the year--is it possible for you to get a gym membership for the winter only, or are there initiation fees that make that cost prohibitive?