When you say bring boots, are you going to bring your own ski boots? Or just snow boots and rent skis and boots?
I'm a notoriously light packer. I'd just roll up my snow pants and jacket as much as possible, no boots, just wear sneakers or even flats into the rental office. And rent skis and boots.
I normally check bags for work travel. It just makes my life easier, because I don't have to haul crap thru airports and security over and over again (for reference, this trip has 3 flights, and 4 security checkpoints).
Think about the decision this way. A month from now, looking back at this trip, will you regret not going skiing? Would you regret going skiing? This idea sounds dumb and obvious, but it's helped me figure my way thru decisions like this...
If the big deal is the checked bag on an international flight (where it's usually free), I wouldn't let that stop me from skiing. Definitely bring your own boots since you'll be much happier with comfortable feet.
Will you get to see your friends another time during the week? Do you get to Munich often to see them? Can they join you on the ski trip. I guess if I had friends in another country that I don't get to see I would want to see them over skiing but if you can do both that would be great.