Why can we perceive frequencies of light?

Special relativity says we perceive any moving object as moving slower and slower in time as their relative speed to us approaches the speed of light.

Doesn't this mean that light, obviously moving at the speed of light, should appear "frozen in time" to an external observer?

However, we do see light oscillating at a given frequency, which implies it's not frozen in time.

I know the Doppler effect exists but I'm not sure how it is supposed to tie in this reasoning. Shouldn't all light be redshifted to infinity by default?