Hi Sarah,
Moving in with someone can bring up some teething problems at first, however if it's fairly new, then you might be able to nip things in the bud before they get any worse.
Many partners don't take the initiative to do things around the house unless asked to or given a list of jobs. I would suggest that you ask him to share the chores with you given that he works less hours- it's only fair. Perhaps you could alternate making meals each night (plan them at the beginning of the week) and set up a cleaning rota so whoever is at home first can get the jobs out of the way.
Snoring can be tricky if you've tried everything. If you have a spare room perhaps you could make that your own- spend some time with your partner so your intimate life is not being neglected and then move into another room where you will get some peace. Perhaps you could ask that he take up the spare room given that he is the one making the noise?
If you think sleeping separately will drive you apart- then you could try some ear plugs, nasal strips or getting him to sleep on his side rather than his back (if this is his go to sleeping position).
Other factors include being overweight, drinking late and smoking- if any of these sound familiar then he may need some support and encouragement to change his ways.
I would also suggest taking the dog for a walk together then it is seen as less of a chore and something you can do as a couple to get some exercise and use the time to talk.
It sounds like you are really frustrated over this- so perhaps wait until it has reduced somewhat and then talk to him. If you try to speak to him about this while you are angry, then it's possible nothing will change.