I'm getting ready to run Icewind Dale: Rime of the Frostmaiden and one of my players is going to be a centaur. Reading over the rules about travel, I see the talk of snowshoes and I have to wonder if the centaur could use them or if they would do any good for a horse like creature. I can't find a ruling anywhere about this, not surprised since it's a very unique situation, and I'm not sure how to base any ruling on it.
First, the rules for snowshoes don't actually exclude their use by horses or centaurs; the rules make no mention of needing to have humanoid feet to wear them. I personally feel it would be poor DMing to just decide that one PC can't possibly keep pace with the rest of the group -- if one PC has to go slow, then the whole party has to go slow, at which point you might as well just forget that snowshoes even exist.
There's no physical reason snowshoes wouldn't work for a centaur. The whole point is to spread out the creature's weight across a wider area to reduce the amount that they sink into snow. Putting a wider base under a hoof would work just fine. While a horse weighs a lot more more than a man, it also has four feet instead of two, so that weight is already more widely distributed. Putting a platform under each hoof will work very well to keep them on top of snowdrifts.
But even better, there is a historical precedent for this -- horse snowshoes actually exist! For an example, this 1555 woodcut from a book by Olaus Magnus depicts a merchant and his horse crossing the mountains in Norway, both wearing showshoes.
They were usually made from wooden planks instead of a rawhide netting we're more familiar with, but anything that spreads out the weight should be fine. Here's an actual equine showshoe from the Norwegian Forestry Museum:
No rule exists to prevent this. Let the players decide.
There is no rule addressing the interaction between centaurs and snowshoes. You will have to decide. In my experience both playing and running this adventure, having one party member be half the speed of the rest would be terrible. The group only moves at the speed of the slowest member. Just let everyone wear snowshoes. Or to put it another way, I find it unlikely that anyone will have more fun because the centaur is slow.
But they might, so just ask your players. Let them decide how they feel about the centaur wearing snowshoes.
What follows is an artifact of a previous revision of the question:
Does a centaur need snowshoes in Icewind Dale?
Snowshoes are required for the travel speed boost.
The Overland Travel Table gives the travel speed with and without snowshoes, and the table description makes no player race considerations:
The speed that characters can travel across Icewind Dale’s rough, snowy tundra is given in the Overland Travel table.
Since the Centaur has no racial traits that would improve travel speed across tundra, a Centaur needs snowshoes to travel at the 1/2 mph speed.
Practically, it probably doesn't matter. If you rule that the centaur needs snowshoes, two pair will cost them 4 gp, which is pretty insignificant overall.
The travel options for Icewind Dale never mention horses, so horses probably struggle in tundra.
We don't see horses mentioned as one of the mount options in the introduction to the adventure. This is not explicitly stated, but it stands to reason that horses are probably pretty poor at traversing the tundra if nobody around the Ten Towns is using them. Based on this, it seems quite reasonable that a horse bodied Centaur is no better at walking through tundra than the rest of the party, so snow shoes are recommended.