If your pets tend to drink from places other than their water bowl, then you need to do a little extra work when setting up your Christmas tree. Chemicals from the fertilisers used on the tree can transfer to the water in the stand, and you don't want your pets drinking that. Image from brendan-c.
Besides the fertilisers, stagnant tree water can be full of bacteria that can make your pet sick if they drink it. When putting up your tree, use a tree skirt or cut a hole in a trash bag to keep the stand covered until you need to water it. Put the tree through the hole, then into the stand. Tape the bag (or skirt) around the stand so it covers the open top. Although this makes changing the water more difficult, it should keep your pets out. For more tips on how to keep your pet safe during the holidays, check out the link below.
Holiday Safety Tips [ASPCA]