I don't know too much about Methotrexate, but know I have severe Crohn's and if not for my fistula my GI would have put me on it instead of 6mp.
Not everyone loses their hair. Some people experience it from prednisone, some people experience it from Humira, or pretty much any of our medications. So it's really up to how your body reacts. What I've been doing recently is taking 1000mcg daily of Biotin to prevent hairloss while on 6mp, and it's worked perfectly! No hairloss whatsoever, when it was terrible on Imuran which is essentially the same medication.