I'm replacing some old cartridge pads that I can't find inserts for with one-piece Kool-stops. Both are asymmetrical types, but the front set of old shoes are explicitly designated for "tail-forward" installation (see image). The only reason I can think of for doing this is for clearance of the fork when cable tension is released. Assuming that this isn't an issue in this particular case (it doesn't look like it would be) is there any other reason to follow this example, rather than installing in the more typical tail-behind orientation that the new pads are designed for? Context is cantilevers on suspension fork brake arch, if that makes a difference.
Some of the KoolStop pads have a ramp at the leading edge (facing in the direction that the wheel rotation comes from – i.e., towards the back of the bike) that is supposed to help sweep water and other contaminants off of the rim. If you have these you'd want to face them in the right direction if you can.
Other than that and clearance I can't think of a reason why it would matter unless the pads are the type with replaceable cartridges in which case you need to make sure that the open end of carrier faces towards the rear so that the pads are pushed forward against the stop.