Managed to climb the entire mountain with 5 feathers. 4 might be possible but I'm not sure.
great game btw
a little exploration game about hiking up a mountain · By
I reckon out of all the tricky spots in the 5 feather run, only one of them would be any more problematic with only 4; that being the first high wall (where the guy sells feathers, also the first spot where it tells you 7 feathers are required). My current strat is jumping around to the left to the bank above the start of the stream, and gliding down to the wall. That gives you just enough stamina to get up the wall with 5.
Can be completed with just 1 feather and under 2 and a half minutes, FYI. ;-)
https://www.speedrun.com/ash/run/y4wxre3m
(Edit) Also with no feather in less than 3 minutes, by exploiting a saving bug.