There is no reason not to increase the fuse size on your battery tender lead if you want to use it for your heated gear too. The wire gauge on that pigtail is plenty big enough to carry 10 amps of current. That would only require a 20 gauge wire, and I seem to recall that they are 16 or at least 18 gauge wires. The fuse is there to protect the wiring harness, not the battery tender, so there is no additional risk there.
I've got a bigger fuse in mine, as many other folks do, so that I can power my electric tire inflation pump without blowing the fuse.