I think kind of what Aida said.
With footwear, first, you don't always have to bookend hair, though it works for me better than wearing very light footwear as a main approach.
But, the "warm" or "cool" aspects are not so relevant for footwear as for tops and toppers which are right by your "head", meaning, skin and hair, in case for example they are in 2 different color directions.
So, I look better in cool colors for tops than a warm cognac or even a warm brown, so while I don't target warm browns for a lot of footwear, just because it's not in my major palette, I could wear those colors in footwear to work with pants or skirts if that makes a good outfit or capsule.
Not sure what colors you think you will be targeting for "face colors" but you still have a lot of flexibility in footwear and accessories regardless. I like adding warm leather tones even to "cool" outfits.