'Willing' is not defined anywhere in the 5e rules. That means the game thinks that the word should be used in the manner of 'natural language'. That does not work for terms like 'willing' (or 'target' for that matter), because the people writing the rules are game designers for Wizards of the Coast (viz. people at the same company and in related roles to the people who write stuff for Magic:The Gathering. For reference, that franchise's current explanation of what a 'target' is is rule 115 and is a little over two pages long) and so have a different definition of those sorts of words than the average non-game-playing person, and furthermore for 'willing' in particular because the philosophy of consent is super complicated anyways and there is no single consistent 'natural language' meaning of the word, even more than for most words--q.v. philosophic research into voluntarism, and/or coersion.
Consequently, any sort of edge-case here is fundamentally beyond the scope of RPGing to determine-- the designers erroneously left out a definition for 'willing' and your group has to add one to make the game playable when what 'willing' means comes up in play, which it will almost certainly do in nearly every campaign.
I will leave the philosophical analysis for discussion elsewhere; you could ask about it here, potentially. That said, let's discuss the mechanical implications.
Unlike in older editions, no creatures in 5e have non-abilities. Skeletons and zombies and golems are, thus, typically just as sentient (i.e. possessed of charisma, intelligence, and wisdom) as other beings, they just are also frequently described as mindless automatons, which is pretty weird. Thus it is unclear if the problem you are describing actually exists; it may be appropriate, depending on how you rule the animation works in each case, to treat them similarly to a dominated or allied creature, assuming you've already worked out what 'willing' means in those contexts.
If you rule that skeletons et. al. aren't or can't be willing from the perspective of their controllers, then those controllers are unable to mount them. This means no riding skeleton horses; doing so becomes impossible:
A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount
(source, also PHB p. 198)
If you rule that skeletons et. al. are willing for whatever their creator/controller wants, the game works fine and seems normal.
If you rule that skeletons et. al. could be willing but aren't in the case of undead if you are their creator/controller because they hate you and want you to die the game gets weird but still works okay and is fun but very grim.