When blocking with a sword while walking on ice, movement is much slower than when blocking while waling on dirt. However, when facing diagonally and walking horizontally e.g. holding W and A, movement is at the same speed as walking on dirt, but restricted (sort of) to horizontal movement. Confirmed with different swords, biomes, game modes, weather and worlds.
Discovered while messing around with soul sand, ice, cobweb, sneaking and blocking.