Rabbits can catch a form of a cold virus.
However the cold virus that rabbits can get is not the same cold virus like the common cold that humans get.
You also cannot get a cold from a rabbit who has the rabbit cold virus.
Rabbits can get a cold virus that is made for them and then if left untreated sometimes the rabbits cold virus can turn into pneumonia.
However most times the rabbit who does have a cold virus are just fine and recover on their own depending on the strain of the cold virus that the rabbit has.
A rabbit may get watery eyes, coughing, sneezing and even sometimes wheezing.