I imagine it's possible for a gerbil to contract a cold, considering that rodents are closely related to primates. But it would be very rare. I've only once in my life heard of a rodent catching a human cold, and it was the class hamster in first grade. If you're a rodent and going to catch a cold, that would be the ideal place to do it.
The rhinovirus is perfectly capable of infecting nonhuman primates, with potentially deadly consequences. This is partly why researchers are required not to approach wild primates. In addition to the potential threat to us, they are in danger of contracting diseases that we carry, to which they have no immunity (including the rhinovirus). Now, with that in mind, it's not a terribly big leap from some of the smaller lemurs to a rodent. Take a look at a Pygmy Tarsier and the resemblance is uncanny, without even looking at the genetics behind it. Although it would obviously be extremely rare, a rodent such as a gerbil catching a human cold would not surprise me in the least.
It would surprise a vet though as we had this converstion with a vet at a recent GP show, it started out on swine flu and then encompassed the issue of viruses in general bottom line from the vet is it is extremely rare for people infected with viruses to transfer it to animals, and the other way as well.