They absolutely can.
There are two types of flea which are generally found on rabbits. The more common is the cat flea, known as Ctenocephalides felides. The other is called the rabbit flea or Spilopsylla cuniculi. It is less common for rabbits to be affected by Spilopsylla cuniculi... C. felides can survive on cats, dogs and rabbits. Therefore, if any of these animals are affected in a multi pet household then there is a high probability of transmission between them.
Various species of fleas have been found on rabbits. They include Pulex irritans, Cediopsylla simples, Odontopsyllus multispinosus, Echinnophaga gallinacea, or Echidnophasis mymecobil. Domestic rabbits are commonly infested by the cat or dog fleas: Ctenocephalides felis or Ctenocephalides canis, respectively.
Most household furries can catch the Ctenocephalides felis. I once had a problem with a lone rat who caught fleas from my cat every few months, though I believe the potential for disease-spreading is worse for rabbits.
It seems the best course of action is to keep vigilant and limit your rabbit's contact with these animals if possible, and continue to treat throughout winter if you can.