This all sounds eerily familiar, OP, but it's a long time ago for me now. The snoring is terrible, my partner also does this, I would sleep in another room with the baby or vice versa and leave him to get a good night's sleep. People on MN are very dismissive about the partner's need to sleep to work, but having crashed my car when sleep deprived, and nearly taking my marriage to the brink of disaster when we were so tired and arguing all the time, neither feeling appreciated, I think sleep is the number one priority to sort out. Just go and sleep with your baby in the main bed/buy a blow up mattress for him/go elsewhere- do you have a spare room?
I would also get him to check for sleep apnoea, but this won't be instant unless you have private health insurance, because you have to have tests and it takes ages to get into a sleep clinic, if you have private, I would go private, but sort out a way in which you can sleep is the number one priority. Competitive tiredness is a well known phenomenon when you have a baby.
For all those shouting-what does he bring? LTB? I am absolutely amazed that you can tell this relationship is doomed from postings of someone who has a four month old baby. All the people I know found the first year a struggle, and plenty of people end up arguing over sleep/childcare arrangements/difficulties in that early period, it's hell on earth. I see nothing unusual in this post at all, the OP is stuck at home doing all the household stuff, he is working very long hours, they are arguing and sleep-deprived. Perfectly normal stuff.
You can work on getting a better distribution of household tasks/roles as well in that first year- he sounds like he is doing some things, so cuddling, taking baby for a while. If you want him to do more, you need to specify what it is you want, (so, do bath and bed on Tue/Thurs) or household tasks, otherwise the stay at home parent can end up doing everything by default.
The MN test, which is a good one, is are you getting the same amount of time off- i.e. without baby, or to pursue your own goals/hobbies? Could you have a few hours off? (you mention going out). Take up the opportunity to do your own things, so it is clear from the start that you are both entitled to time off, and on weekends, childcare/household stuff/time off needs to be shared.
I think it is far too early and there is far too much potential to change to worry this is all a disaster, plenty of families take time to adjust (my husband was really useless with my first child, but is now one of the most proactive child-oriented dads I know and took a year off when my second was born).