Levels of most resorts (1000-1800m) are ok but going up mountains in, for example, a cable car could cause ear pain due to pressure changes and you need to be aware of the drop in temperature as babies can lose heat quicker and are less active. Also the air can become "thinner" affecting even adults with lightheaded and drowsiness so there may be a increased risk of SIDS with prolonged exposure. We were advised not to take an under 2 up the Aiguille du Midi in Chamonix (3500m).
If you are staying at anything over 1800m (ish) and have children under 18 months (again ish) it might be worth having a word with your GP. Essentially infants might get a bit of altitude sickness (headaches, short of breath etc). Unlikely if children are fit and healthy but one to be conscious of.