here in Scotland it also coincides with the older festival of Beltane,
Sorry, neither Easter nor Midwinter coincides with Beltane, which is halfway between Spring Equinox and Midsummer (and usually calendarily celebrated in or around 1st May*).
But, yes, Beltane is a Fire Festival, fire doesn't necessarily mean winter, the Japanese prefer their fireworks for summer, not later autumn for example.
* Do the conservatives still want to abolish Mayday for it's acquired socialist associations and replace it with something tacky, empty and artificial like Trafalger Day???