The ice box is it even 4'x4'?
I would think your skids would be digging in my woods as I don't have smooth paths to drag a blind down. I used treated 4"x4" skids the a 45 degree angle on both ends so I can tow the blind either end.
Yes I can not tow then on side hills or up and down hills unless the house part is on the up hill side.
Al