age limits on booking a hotel

hello.
i have 2 questions i would like to know..

1. I am planning to travel by train from sendai to sapporo in the first week of december, I have heard it is extremely cold and harsh snow conditions in this time, and is it still ok to catch the train there?? or will the tracks be closed from snow??

2. Also is there an age limit to book a hotel or even an hostel in that matter?
My friends and I are only 17.
Also last time I went to japan the hotel always check your passports.
If i cannot book a hotel on my own, my parents will have to my credit card, what happens if the hotel staff check our passports and relised noone is over 18 let alone 20 or 21!!
thanks

I am planning to travel by train from sendai to sapporo in the first week of december, I have heard it is extremely cold and harsh snow conditions in this time

That is exaggerated!

Temperatures in Sapporo hover around zero. Only seldomly fall they below -10. In Sendai, temperatures barely fall below freezing. There might be some snow in the Sapporo area, but probably no snow in Sendai.

Even if there was lots of snow, trains between Sapporo and Sendai will be running and are heated.