Maybe, but just because it isn't easy doesn't mean they can't do it.
I didn't say they couldn't do it and you know I didn't say they couldn't do it. Here's what I wrote:
There is still the issue of the stairs. Average tread depth is less than 12." A large inn presumably has rooms on the second floor. The centaur can go up the stairs but damn if he isn't going to have a bitch of a time coming down the stairs.
Difficult, not impossible.
You want to play a centaur? Fine. Have at it.
First, give me a DC 15 DEX check to go up the stairs. Fail by more than 5 and you break a tread because you weigh 2,000 lbs. It's not a question of can a horse walk up stairs; it's a question of whether wooden steps can hold a horse's weight.
For comparison, 29 CFR 1910.24(c) states; "Fixed stairways shall be designed and constructed to carry a load of five times the normal live load anticipated but never of less strength than to carry safely
a moving concentrated load of 1,000 pounds" [emphasis added]." Therefore, with respect to the design calculation, the normal live load is spread over the whole stair tread area and the moving concentrated load is considered to be a point load applied at a location on the stair system where the maximum stress would be experienced by the system (the 1000 lbs loading criteria is a minimum).
Now, are this inn's stairs up to OSHA code? (fun exercise: read about moving long gun safes into basements - the safe weighs 1,000 lbs and the people weigh another 600 lbs)
Mazel tov! You made it upstairs. Now, give me a DC19 DEX check to come down the stairs. Why? Again, because you weigh 2,000 lbs and are now trying to walk down those wooden stairs with the lower body of a horse. You are trying to put your hooves on 11" treads (at the deepest) and assuming the risers are even. If the treads are shallower, maybe a DC 20. If the risers are uneven, DC 22.
Can a horse walk up stairs? If the stairs are strong enough to hold a horse, sure, with difficulty. Can a horse walk down stairs? Yes. With extensive training. Without extensive training, it's damned hard to do and a misstep will cause injury to the horse and the stairs.
Like I said, the centaur is going to have a bitch of a time.