small dogs are notorioius for that; could be also that, like with my lilee, we allow her to use our bathroom as hers when it rains, as she just wont go outside, at all. so easier for us that its also considered 'outside' . useful for when we cant get back and dont have a dog sitter, they both know that the bathroom is also theirs if needed. the male usually doesnt , she does.
cold could be a factor but also the main mistake that most people make is that once the dog does its thing outdoors, they all come bakc indoors. so the dog has learned that poop= go back to boring inside.
so u have to teach him basical to poop on commman. everytime he poops, reward adn use a command like: potty, or peepee or toilet time or what ver word or languagte u want to use, always use that term, while he's doing it... even if it means that the first week u are sitting and walking with him for an hour or more... he will eventually go (a few raisins or oil in his dinner will help with the process)... once he goes, u say 'billy, poopoo" or whatever, while giving him a rinky dinky itsy bitsy reward/or his fave toy if thats what turns him on... then, KEEP GOING FOR AN OTHER MINUTE OR TWO on the 'fun' walk, THEN go home to house. dogs are sooooo good at training their pets oops owners to keep walking for ever and not go home... so first, a poo and pee, then play, then home. always. so that when its horrible outside or u are in a hurry, u just say, 'teddy make pooo' and he does.
my boxers, fox terrier and now the lhasas go on command. then we can go off and play or fun walk. just like a child pees before a long trip. (hell, i make my hsuband pee before a long trip even when he tells me he doesnt have to go, cause always but always we hit the troll way, and there its illegal to stop the car for anything other then mechanical trouble)...
it could be there is no comfortable place for him to poo outside. lilee cannot deal with unlevel surfaces, sand/rocky. only flat dirt. so we have an area outside that is her toilet of choice. so in the morning when im in a hurry, we go the doggy toilet area only.
maybe he was spoiled and carried everywhere by his first owner? maybe never had been outdoors? or some dogs only are used to certain surfaces. my boxer was used to sand and dirt also, but in a kennel she had issues with a cement run. (we are fairly rural in set up here, not much road or cement).
moving his poo outside and making it his toilet is a good idea. mean while wash the bathroom with white vinegar . bathrooms smell just like bathrooms, to dog noses. it smells like pee (men drip, etc) and the molecules stay in the floor and around the toilet so its obvious that he would choose there. whtie vinegar is good for that. rugs are also like dirt or grass...
we aslo have a closed door policy hwen we arent in the house. prevents doggy misunderstandings of what is off limits when.
u can teach dogs to ring a bell when they want out, just like scratching at the door, or whatever. lilee tends to stand and stare at us from the hall area when she wants out, she's not a very 'cuey' dog. foofoo will whine and scratch at the door. the boxers would stand up and try to open the door. my friend's saluki rings a bell at the door. it could be that he is trying to get your attention to go somewhere, without u noticing cause he is small and u are misreading his intentions. does he stop and stare and then run to the bathroom, if so, run after him, pick hm up (yep, might get pee'd on, been there done that, or pood on , even worse), take him outside, say 'teddy go poopoo' good boy, treat, even if he he doesnt really continue...
they say lhasa apsos are really really slow about potty training (yes, they are very very slow) but eventually they get it. they just do not have the 'want to please' attitude, and they are small so u dont notice whent they squat, as pups, and with all the fur, until u realize they are peeing its too late... but eventually they do learn.