Outpatient clinics at all hospitals in South West Wales are now running normally with planned surgery is also going ahead as usual.
However, some individual operations may be delayed because of increased pressures, particularly at Morriston and the Princess of Wales hospitals.
A spokesperson for ABM advised anyone affected to keep in contact with the hospital for updates.
"We are also experiencing an increase in the number of people arriving at our A&E departments with injuries from slips and falls," a spokesperson said today.
They advised: "Please remember to take great care on untreated surfaces, including icy paths and driveways around your own home.
"Many people fall and hurt themselves putting out the rubbish or doing other household chores."