Many of the people attending the hospital units had injuries related to the ice, according to the trust.
Patients in need of urgent care for injuries were asked to attend A&E instead, where additional staff had been brought in to manage demand.
“We have put in alternative plans to ensure patients can still get the care they need,” the spokesperson said.
“We will prioritise patients based on clinical urgency and whilst our teams are working hard to treat people as quickly as they can, there will inevitably be longer waits for less urgent injuries today.”
The minor injuries unit is expected to reopen as usual at 08:00 GMT on Thursday.