I did my undergrad at Madison. I got into the Natatorium pool ONCE during one of my rehab periods, swam for 50 minutes, and basically came out with hypothermia. I swear, that pool is kept at preserve-dead-bodies temperatures. I don't know about the SERF one. I have used the YMCA west side pool for two different stretches of time and honestly, I really like it. The Y isn't that expensive and is very serviceable; I recommend checking it out. Hell, their weight room isn't that bad, either. I mean, I've seen worse. I guess that's not saying much. Let's try: it's not Planet Fitness.
It really just depends on the nature of the injury. The rule here is that if you can do it and cause yourself no pain, you're probably okay to do it. This is what some of the members of our team have done during certain injuries that prevented them from back squatting because of pain. I don't know exactly what's going on with your lower back, so I can't say for certain, but I will say that it's worth a try. And let's say you can do it--awesome! You've just learned a good variant to use in support of your regular back squat for the future--a front squat can be a good way to give your lower back a break, fortify core strength gaps, and work quads if you feel like your quads need extra emphasis.