Hi Kristin,
One of the two waterparks (Typhoon Lagoon or Blizzard Beach) generally closes for refurbishment at alternating times during the winter (usually January or February). The other park is generally open for guests to enjoy. The best place to check which parks (or specific attractions within a park) are closed for refurbishment is on the Disney World "Operational Updates" page, which you can access by clicking
HERE.
If your kids cannot swim, they can still enjoy the parks. If they are small, each waterpark has an amazingly well-themed area for kids under 48 inches. Blizzard Beach has "Tikes Peak", which is essentially a scaled-down replica of the larger park, but for small kids. It has slides, tube rides and a water-spray area. This area is very well shaded and also has sand for the kids to play with. It is, by far, my family's favorite spot in the park. Typhoon Lagoon has "Ketchakiddiee Creek", which has sides, fountains and a "mini-rapids" for smaller children.
In both parks, life jackets are available for children and adults free of charge for use during the day. My kids can both swim, but they certainly can't hold a candle to Michael Phelps, so I require them to wear them in the larger pools and on some of the "crazier" slides...just in case. (This is a MOMS panel, remember!) Each ride has its own height and other restrictions posted clearly to ensure that guests are safe. Most of the slides empty into relatively shallow water. The wave pool at Typhoon Lagoon is an area that I would be most careful that non-swimmers stay in the shallow area, mind the waves and wear life jackets, as appropriate.
If you chose to go to Blizzard Beach, try sharing a "garbage pail". It's a giant ice cream sundae served in a sand pail. We never go home without one!