They have a weird animation but they can't walk on ice blocks. Though they can jump on them.
MC-251931
Frogs can't walk properly on ice, blue ice, packed ice, frosted ice and soul sand
Open
7
(Unassigned)
Confirmed
Gameplay
Low
Textures and models
1.19 Pre-release 1, 1.19.3, 1.19.4 Pre-release 3, 1.19.4, 23w18a, 1.20.3 Release Candidate 1
Retrieved
This also appears to be the case with turtles. See MC-201774.