. I would use 10w30 synthetic oil in the hydrostatic transmission
If the system is designed for 40 when hot and you run 30 when hot you will loose drive when you need it most like shifting snow or working soil.
Every second that it is running hot more oil will be flowing out the sides of the swash plate in place of through it and once you get a little wear there the whole system goes downhill fast.
A thinner oil can 1/2 the life span of the transmission and you are talking $ 1000 for a repair.
Trannies are even worse because they don't blow smoke or give any sign of a problem till you put your foot down & it does not move or just crawls by which time it is too late to save them.
If the oils in the first post were correct the 15W 40 would be for places where you don't move snow.