I don't see any major problems, as the chromatography columns and resins are known to work in refrigerated environments. Avoid abrupt temperature changes, as they might affect the bed structure of your columns.

Temperature changes, however, might precipitate salts and buffer components which then may cause trouble, esp. if that is happening inside pumps, valves or tubing.

If you don't use high flow rates, all liquids should reach room temperature quickly while being pumped through the tubings, so if you don't see dew precipitating on your equipment, you should be fine.

Low ionic strength, however, might precipitate some proteins you actually want to get rid of. Maybe better use PBS or saline instead of water.

Thanks a lot, Wolfgang!