I am looking for suggestions on how to train a young adult cat to use a
litter box indoors this winter, instead of doing his business outdoors.

My wife and I adopted (or were adopted by) a semi-stray cat in our
neighborhood this Summer.  A nearby family had been minimally looking after
this cat until now, and told us that the cat would use a litter box if
needed.  As the weather in our area has turned colder, we have been keeping
our new cat indoors during the night.  So far, we haven't seen any evidence
that the cat is inclined to use his litter box.  Instead, he prefers to go
outside, usually at 2-3:00 AM, and wakes us up to let him out.  So far,
there have been no 'accidents' in our house.

The cat is 2-4 years old, as nearly as anyone can guess.  He has been
neutered.  He prefers to be outside during the day, and spends the majority
of his time sleeping on our back deck. We own a house, and have tried
placing the litter box in both a basement utility room, and in a bathroom.
We have shown the cat his box on numerous occasions, without results.  We
have tried brands of litter that claim to attract cats, and we have even
seeded his box with a few samples of  his feces so that he would identify
the litter box as his, and get a clue about its purpose.

I would greatly appreciate constructive suggestions about other approaches
we might try.

spburrows@cox.net