There are some rare cases where the rate of product formation decreases with temperature, but you probably don't need to worry about them. In chemistry there are always exceptions to every rule.
Regarding your freezer question, it depends on what you mean by "problem". In most cases there won't be a safety issue but quality of the product can definitely change due to certain physical processes that can occur during freezing (precipitation, crystallization, evaporation). These processes can affect texture, color, and water content. "Freezer burn" is one you've probably heard of. Also if you've ever frozen and thawed a banana, you know what I mean.