Does such a job exist?

A place that big? I wondered the same thing. But it would save money, and I guess since on one is around, there's no real challenge. So, maybe so.

It seems like a person should have a background in carpentry, electrical, plumbing and HVAC for a job like this.

I'm still looking for one of these jobs.

There are plenty of large apartment buildings that have a single caretaker even with the units occupied all year round. With a hotel that is well maintained I think it would be less work to watch it over the winter considering the wear and tear element is gone. The rooms are all empty with the power off, heat to everything is supplied by one boiler.

I'm surprised the hotel would outright close in the winter at all. Places with snow attract winter recreation guests for skiing, snowmobiling and just cozy getaways. Maybe that was different in the late 70s/early 80s, but skiing was definitely a very popular sport at those times, as was snowmobiling, although less popular than skiing.

even if a one-man job like this existed, i highly doubt they would hire a drunk writer instead of an ex-cop or someone with HVAC experience

I think they would require 2 people, in case of a medical emergency.

I once worked nights in a hotel on the desk , after everyone had gone to bed I'd just bum around drinking beers from the bar and watching movies good job but paid little , anyway sometimes I was completely alone in the hotel and no guests there when major renovations took place but still had to have one person in the building at all times due to insurance reasons so maybe that's a universal thing

I heard of caretaker jobs on isolated islands:
https://findislands.com/private-island-caretaker-how-to-settle-on-a-private-island-and-get-paid-for-it/