Are semi-frozen meat and vegetables safe to cook? My refrigerator maintains a temperature between 0-5 degrees C. However, I quite often find that carrots, mushrooms etc. stored in the salad drawer are either coated in ice, or semi-frozen. Today I found some chicken that had been stored on the bottom shelf semi-frozen and quire hard, although sliceable with a knife.

Is it safe to cook with these items?
Sure. What would make them unsafe?  We freeze to preserve food all the time.  More importantly, this freezing will likely impact the quality, especially the vegetables.  I am guessing there is likely some freeze and thaw, which is not good for storage, as the ice crystals damage the cell structure of foods.  However, as long as you cook the chicken properly (to the appropriate internal temperature), there is not a safety issue.  Maybe adjust your refrigerator settings so that this doesn't happen...or store vegetables in an alternate location in your refrigerator.