We've a few rescue cats - we got them all when they were about three / four years old. We kept them inside initially for six weeks or so, made sure that they'd got used to living in a new house before we let them outside.

The one which had been abandoned and had been living outside for a few weeks (a boy) stopped using his litter tray completely, as soon as he was allowed outside again.

The other two, both girls but a 'smooth' changeover, took a bit more time to get used to being outside. One transitioned off of her litter tray after a couple of months by herself; the other took more like four months, and she was a bit of a fair-weather pooper for a while as well.

My take-home message would be that cats generally prefer to do their business as far away from where they live as possible. Only possible bit of advice would be to wait until the weather's getting better in case your cats dislike the wind and the rain. I believe forest cats love the frosty weather anyway, though?