The reason people freeze hamster food is because there have been occasions of moth outbreaks. Nearly all pet foods contain moth eggs (grim I know) which are too small to be seen by the human eye, They are dormant but in particularly warm weather they can hatch out if you're unlucky! Freezing food for at least a week, kills the eggs. With things like hay there can be little mites etc so it's a good idea to freeze any hay as well, so freezing sprays would be a precaution too. It's a pain when you want to use something straight away as well! But with the food, you could put the bag in the freezer for a week and just take out a daily amount each day for that first week - at least it's had some freezer time and will probably be fine. It can help to always have two bags so one is in the freezer ready to use when you finish the first bag.
What hamster mix have you got for him?