I am dealing with my first youngster (7 yo exracehorse) at the moment.
I have a 30+ yo rescue mare who needed a horsey friend. When she arrived her feet were dreadfully overgrown and she was lame in front. She is now feeling great and often bucks for joy, sometimes when I'm riding her.
A weanling will need supplementary feeding every single day to give best chance for full growth and development of horsie. Be prepared to pay for a special diet and make sure you are close enough to pop in at least once every day.
Did you know that a 1 yo horse = 8 yo human and 2 yo horse = 13 yo human (I think, don't quote me on that). It's a very important time for a horse. It's when they get their start.
Good luck finding a suitable horse.