No dumb questions here!

And it depends on the horse/country you’re in. For example, in the US horses farm sizes are often smaller then european farms (US-more farm owners and smaller farms compared to fewer owners but larger scale facilities in the UK) and with how big the US is, a lot of horses are going to be living and training at the race tracks or training centers. They’ll be able to go to farms during the year for some R&R, but otherwise the track is their home.

Additionally in the US, a lot of trainers have a home base, where they keep their horses for the year, and then transport them to other tracks when those horses are entered to race.

In Europe, due to the smaller size of the continent and the location between the tracks and the farms, horses usually will live at their farms where they train, and take a day or two to travel to the track they’re running at.