Having an onsite rink is still a huge advantage. If you look at Google, the rink operates from 9am to 8pm and is closed on weekends.
Ingalls Rink
73 Sachem St, New Haven, CT 06511
(203) 432-0876 https://g.co/kgs/to3acf.
Only if they could hire one person to operate the rink some extra hours, say 6-9am to accommodate Nathan's personal training, enough ice time is almost guaranteed. Even better, he doesn't have to share the ice. Nathan can still find plenty of time during the day for his off ice training. As long as he's provided with right resources and good planning, I think double duty is quite achievable.
The Collegiate Yale Figure Skating Club has freestyle sessions on Sundays. But given Yale's endowment, I'm sure they could hire someone to work at the rink in the morning. The greater problem would be to take time away from their ::cough:: mediocre ::cough:: hockey team.