Lol sure they can. Just as with us humans there are different reasons why.

It can be caused by an infection, like when we have a cold and cannot breath right.

A tumor in the respiratory system can also cause snoring.

Often with certain breeds it is caused due to torture breeding. Short headed breeds like bulldogs and pugs are often suffering from it. Their soft palate is often too long and that causes snoring. Same with humans if their soft palate is not trained well, so to say.

Also when the vocal cords are weak, snoring can occur.