You do tend to notice the haloes, mock suns etc. more when the sun is lower in the sky. But I get the impression that, here in Northern Ireland, they're not more likely at one time of year than another ... we get loads of cirrus throughout the year,
Not exactly. I tended to notice that cirrus (here in Poltava) are a usual thing on a clear winter day, but a bit rarer during autumn/spring, and much rarer during summer.
Well, I speak about something like this one, captured in early March

sometimes (as for instance last night) it is very obvious that this cloud is smeared out jet contrails, and we have the misfortune to live underneath one of the busiest air routes in the world - all the jets between Western Europe and the USA pass overhead.
Thin high cloud allows solar heat in but traps the escaping radiation from the ground. Hence it increases the greenhouse effect - it's been estimated that a jet aircraft leaving a persistent contrail contributes at least ten times as much global warming that the effect of burning the fossil fuel has. The pity is that, by flying lower and slightly slower, the aircraft would use a few percent more fuel .... surely worth the investment for the sake of a large reduction in climate change and the beauty of the clear night sky.
Unfortunately, it's truth.

Jet aircrafts is another serious reason of global warming. I think it is necessary to reduce an amount of flights.