We have several outside cats - they would be welcome in the house but they won't come in, they were feral strays who we have gradually tamed.
They sleep in a purpose built shed with small sleeping compartments and heated electric pads which they love. We also have insulated beds in there which they can use if the heated pads are off. They must be cosy because I often find the house cat sleeping in there and he has the run of the house and can sleep anywhere he wants.
As an alternative, though, have you considered changing the cat flap to a microchip controlled one? They're more expensive but you can program them to your cats' microchips and they would be the only ones let in. Many posters on here use them and have found them to be really effective.
Our cats spend night times in the conservatory, they have a cat flap so can come and go as they please but other cats are now constantly coming in and spraying everywhere
I'm thinking of losing the cat flap and letting the cats in and out of the house during the day and at night putting them outside but with a decent cat shelter to sleep in, preferably a heated one.
Does anyone use one that they could recommend or will it be horrible for them?(our conservatory isn't heated so does get pretty cold but they have a heated pad to sleep on). I only want to do it if they can be comfortable overnight in an outdoor shelter.