Another enabler for another pair of boots! Even if you don't wear them straight away, it would be safer to keep a backup pair in case something happens to the current ones (I imagine it would be no fun to be left with NO snow boots, 'ugly' or not, in deep winter!) Not in black though, to expand your options.
As for the bag, a washed black sounds like a good idea given your current collection. But I think a burgundy might read as a 'colour' with the rest of your clothes - if that's what you want though then go for it! But I imagine it might be a little less versatile for someone who generally prefers to dress in neutrals?
How about a bag in a cool beige or tan instead? Cognac could potentially work with your hair too - make sure you bring one of your workhorse coats/ puffers with you when you shop for the bag though, to check whether the colours 'go' but also to ensure the strap extends long enough to be worn over your coat!