I've done the 3 Peaks twice, once there was snow on the tops, the second time it was a heatwave.

Shoe wise, the first time I wore Walshes and had really painful feet coming off Ingleborough - do not underestimate how far it is to Horton from the summit! The second time I had a trail shoe with some padding. There isn't much "soft" ground on the route and your feet take quite a pounding, even when you are on the grassy bits there's rock not far beneath the surface.