Some kinds of frogs freeze solid during the winter and then thaw in the spring. As the freezing progresses, blood circulation stops. How would you expect cells not being served by the circulatory system to produce ATP during this time, and what by-product would you expect to build up in the cells?

fermentation and lactate

Explanation:

Substrate level phosphorylation  as Glycolysis  takes place. This is because this is a pathway of energy production which occurs  without  the  presence of oxygen.(since circulation  has  stopped oxygen supply has seized).

Therefore the pyruvate produced as product of glycolysis will be converted directly to lactate in a single step reaction  by Lactate dehydrogenase  enzyme in lactic acid fermentation.With lactate produced as the waste product.