Qustion
Why do they recommend that the battery be removed from the vehicle if left on a long maintenance charge?
Extremely cold batteries do not accept a charge well (if at all). Of course, they also don't lose their charge or provide energy as easily either. Charging a "frozen" (very cold) battery can damage the battery and even be dangerous. However, that is only at high charge rates... doesn't apply to a trickle charger like a Battery Tender.
In any case, I never remove my battery from the bike, I just hook it up to the Tender and leave it alone. Never had any issue. But do check the light the next day to make sure it turns green and stays green. If it seems to stay solid red, unplug it for a dozen hours or more, then plug it back in and see if it returns to green after several more hours or the next day. Once it is green, forget about it.
NEVER leave the battery charging for days and days on red. The Tender should not allow that to happen, but I think it can start to occur on some batteries with questionable service life remaining.