It sounds like they wanted to make it look like theirs and I wouldn't be happy about it.
I know people are saying these things don't matter, don't worry about it but other people will take the piss and claim things as theirs when they aren't. This can be where it starts.
I agree with this. It had only been painted a year ago, so was highly unlikely to need repainting. I think the new neighbour is wanting to assert their perceived authority and is probably the sort you want to watch out for. They definitely didn't see a job that needed doing and just get on with doing it - they went right ahead and made a change that they wanted. I'm not one of those who thinks that new neighbours should have fewer rights e.g. "the old couple who lived there before for 30 years didn't have a car, so the man from number 17 parked on the road outside their house, so it's 'his' space and you can never use it" - but it's outrageous to just move in and start making changes to communal/other people's property without asking/mentioning it to them. That sounds like the actions of the tiresome self-appointed 'road/village/community leaders', although they have at least normally lived there for a long time and know the score.
It might be a genuine misunderstanding, or it might even be that the estate agent lied to them and said it was theirs; however it could be that they're obstinate and/or dim and have extrapolated that 'this is the gate to our property' = 'this is OUR gate'. We see enough threads on here about shared drives and the like, where this is clearly the case: some people are too stupid or selfish to realise that 'this is ours' but it's also just as much theirs.
That said, I'm not convinced that the gate is actually shared - it seems to be your gate. They own the access rights but may well have no claim whatsoever on the gate.
I think those calling you boring, telling you to get a life, wishing they had similar 'non-problems' etc. are being quite naive. Apart from it sounding like it is YOUR gate - so how would the neighbour like it if you just arbitrarily went and painted his front door a very different colour (or even repainted it unnecessarily in the same colour)?
I wouldn't make a big fuss about it, but I would go over and make it clear that, whilst you have no objections whatsoever to their right of way, you're not happy that he painted YOUR gate, so please don't do something like that again. Don't add 'without asking/checking first' as he shouldn't be doing it at all. If you say nothing, they'll take it as acknowledgment that they can do what they want, maybe even use it against you in future in any access/land grabs: "Well, if it had been their gate, as they seem to think, and not mine, surely they would have objected when I painted my gate shortly after I moved in". I'd keep a very close eye on this one.