How do you go about naming seasons and months in a fantasy novel?

This is something that has been on my mind for as long as I have been working on my fantasy novel and I still haven't figured it out. I'm quite sure that I'm far from being original when I say that I want to go with 'moons' instead of 'months'. I understand (or am I wrong in my assumption?) that a lot of authors who write High Fantasy prefer to go with 'moons' and no wonder. I think that 'moon' sounds much more poetic and mysterious than 'month' and, therefore, serves the purpose of furnishing the fantasy world much better. But there are other questions to consider... Should I have four seasons or two seasons? Should I use the established names for them (winter, spring, summer, autumn) or come up with my own? And what about the names of the months? It doesn't matter as far as my novel goes – my characters don't talk about seasons and months - and I think I make it clear that it's set in spring through description. However, as an author I feel it my duty and obligation to know such things.

Many years ago I actually came up with the list of names of the months/moons for the fantasy book I was working on back then - gradually, after years and years of countless drafts and revision, it transformed into the book I'm currently trying to find an agent for. Also, I've recently discovered the list of names of the months given in Farmers' Almanac I hadn't heard/known about before. How come I hadn't, though?! It was established in 1818! That's my favourite time period as far as novel-writing goes - well, as long as the action doesn't take place in the fantasy world of my own creation, of course! Anyway, it turned out that some of them sound kind of similar to mine, which, I suppose, is hardly surprising, considering that I based my names on certain distinctive characteristics of each month and season. So the question is: should I use the established names or my own? The established ones offer a much broader vision and bigger choice than my own, however, I could work on that. In any case, here are both lists:

Month	Farmers' Almanac (one version)	The name I came up with
JANUARY	Wolf Moon, Old Moon	White Moon
FEBRUARY	Snow Moon, Hunger Moon	Stormy Moon
MARCH	Worm Moon, Crow Moon, Sap Moon, Lenten Moon	Floods on the Run Moon
APRIL	Seed Moon, Pink Moon, Sprouting Grass Moon, Egg Moon, Fish Moon	Sunny Moon
MAY	Milk Moon, Flower Moon, Corn Planting Moon	Buds in Bloom Moon
JUNE	Mead Moon, Strawberry Moon, Rose Moon, Thunder Moon	Flower Moon
JULY	Hay Moon, Buck Moon, Thunder Moon	Shower Moon
AUGUST	Corn Moon, Sturgeon Moon, Red Moon, Green Corn Moon, Grain Moon	Harvest Moon
SEPTEMBER	Harvest Moon, Full Corn Moon	Yellow Moon
OCTOBER	Hunter's Moon, Blood Moon, Sanguine Moon	Misty Moon
NOVEMBER	Beaver Moon, Frosty Moon	Rainy Moon
DECEMBER	Oak Moon Cold Moon, Long Nights Moon	Cold Moon

I mean, look at all these lovely names! There's enough to choose from without coming up with your own stuff - unless you want to, that is. Then, of course, there is another possibility: to name the moons of the year in honour of female rulers in that fantasy world of mine. But I think I actually tried doing that once and I had to give up in the end, because I found that it was extremely difficult to transform most proper names into the names of the months without them sounding completely ridiculous or awkward.

So what do you do, fellow authors? If you write fantasy that requires name change for seasons and months, how do you go about naming them? Does it even matter in the long run (for readers) what seasons and months are called?