"We have three horses."
Translation:Üç atımız var.
Why can't I say 'Uc at bizde'? (my keyboard doesn't let me put in turkish characters)
That would make the horses definite. It would mean "we have the three horses".
Good to know! Thanks! So, whenever I use that formation (bane, sane, bizde, etc) is it always for something definite?
Because "var" literally means exist. The most literal translation for "3 atımız var." would be "Our three horses exist." For the literal translation for "We have 3 horses" would be "Biz 3 at bulunduruyoruz." It is very complicated for English speakers, but mostly the 1st one is being used.
Would "biz üç atlarımız var" also be correct? I am confused that it is plural without the lar/ler ending
No, it wouldn't. Numbers are followed by a singular noun. The plural ending implies that there is more than one horse. But that was already crystal clear the moment you said "three", so an extra plural suffix is pointless. At least in Turkish.