Wintermoor's "funding issues" were from Enfield pouring money into the future Ultimate Club.
He repeatedly states his intentions to support the Tactics Club after they complete the ritual to protect others from the Gatekeeper. And dialogue during the epilogue mentions that the Equestrian Club is going to get a horse again, so the school has some money.Enfield was likely putting a lot of the school's money aside to support his eventual successors financially, removing a burden they could face. This, unfortunately, lead to some clubs (like the Equestrian Club) losing funding for any club activities. The skating rink really was meant to cheer up the students.
Enfield hoped that students having fun would generate enough positive energy to keep the Gatekeeper from being able to prey on them until he could find a successor. Unfortunately, the lack of funding meant the skating rink was in a sorry state, so that plan failed.