A few years ago I started my own tradition of going for a ride to Dorset on New Year’s Day, and so drunk drivers was something that initially worried me. But I saw nothing worse than on any other day, and none of the worst driving I have experienced was on that day.
So I would advise to be extra careful and observant just in case, but do not let it stop you going out.
At least in normal times.
Aside from the risk of poor ambulance response should you have an accident, it also seems selfish to needlessly risk needing medical help at a time when it is so strained, potentially preventing it going to someone else.
Having spent literally half the year housebound to shielding, I have separately wanted to be able to get on my bike. And I can easily rationalize it as being safe when I will be alone and isolated in safety gear. The only risk being having to buy petrol, and I can reduce that by using pay-at-pump stations. But I did not, because I did not want to risk taking up an ambulance or hospital bed.