The rhyme:

"A cow with its tail to the West makes the weather best, A cow with its tail to the East makes the weather least"

The reason:

This alludes to the direction in which the cow faces in the field as a sign of weather to come as cows typically stand with their backs to the wind.

Westerly winds tend to mean arriving or continuing fair weather and easterly winds usually indicate arriving or continuing unsettled weather. Therefore a cow is actually good a way as any of knowing what the next few hour's weather.