Refinishing furniture in a space that is below or above the 65*-75* F range can lead to problems, and a space below 55* F is definitely too cold. One issue caused by cold temperatures is the development of dimples in the finish called "Orange Peel".
The colder your space it is, the longer you have to wait between coats. Cold temperatures slow the dry time and affect how quickly the finish will level and harden. Our easy rule of thumb is; if it's cold enough to wear a sweater it's too cold to apply a water based finish.