Main Canon
Within the main canon there are no examples of the Borg successfully assimilating anything other than sentient, bipedal, humanoid creatures.
That being said, there's no reason to assume they couldn't assimilate them, if the mood took them and they saw a benefit in doing so. Otherwise they'd just ignore them or kill them if they presented a threat.
Extended Universe (EU)
Within the novel The Return (written by none other than William Shatner) PIcardPicard encounters some assimilated dogsdogs.
Two dogs—sleek Dobermans, pets of the personnel who had been assigned here, no doubt, trotted past. But they did not stop to investigate. Bioneuronic implants studded their skulls. Biomechanical tubes were grafted to their chests.
One dog turned to look at Picard as it passed. One eye clear though expressionless, so unlike the breed. The other eye had been replaced by a laser sensor.
