And hardly any other holiday has any?
There are probably hundreds of Christmas songs that we hear every year. Hannukah has many songs, which probably due to occuring around the same time as Christmas. But do you ever hear any Halloween or Easter songs? Maybe once in a while, but there are just so many more Christmas songs? Why is that?
Hmmmm…well, consider. Christmas was a caroling holiday. That is, a getting-liquored-up-and-going-around-singing-at-the-gentry-till-they-give-you-food-and-money-and-more-liquor holiday. Plus it’s a good way to keep warm (along with being liquored up). Singing has always been an integral part of Christmas. So we have a lot of songs handed down.
And then we went from there.
As I understand it, the whole caroling/singing aspect of Christmas nearly died out for a while (after the Reformation and through the 18th century), and was then resurrected through the efforts of some enthusiastic Victorians. Then it caught fire, so to speak. Meanwhile, we pretty much stopped singing in the streets at any other time.
Carols are technically a particular type of song, to quote from my Oxford book of carols:
Anyway it goes on for a while about the history of carols and caroling, and I’m sure you could get it at the library.
Once upon a time there were, in fact, carols for different times of the year. This book I’ve just quoted from contains carols for all sorts of themes and a liturgical calendar showing appropriate carols for Lent, Easter, spring, summer, harvest, autumn, winter, and general uses, plus a bunch just called ‘legendary.’
But now, the word ‘carol’ is associated only with Christmas songs, whether they belong to the category of carol or not. We would probably think of these other songs as folk-hymns, and if anyone still sings them it’s in church or Ren faires.
It is the season to be jolly, after all 
Actually, there are a good many Easter songs, but they’re called hymns, and you generally have to go to a church to hear them. (I recommend “Christ The Lord Is Risen Today”.) Handel’s “Messiah” is at least as much Easter as Christmas music; the “Hallelujah” chorus celebrates the Resurrection, not the Nativity.
Of course there are few or no secular Easter songs other than “Easter Parade”, but this is because there are few secular customs around Easter other than egg hunts and candy eating, and those are pretty much limited to children. Certainly there’s nothing resembling the orgies of decorating, feasting, partying, family gatherings and gift swapping that have gathered around Christmas. This means there’s little money to be made off of Easter, so there’s no incentive for Easter music to be incorporated in TV ads and played in malls.
I dunno about that, IME Easter seems to be approaching Christmas in its secular, commercialistic frenzy. People decorating their lawns with those godawful Easter egg trees, pre-made Easter baskets worth a mindboggling amount of money… It’s obviously not there yet, but it’s on its way.
I don’t think Easter ever cost my folks more than 10 bucks for me and my brother together. Some fake grass, a chocolate bunny and a handful of smaller candies, and a dozen eggs to dye with food coloring. Nowadays, there’s a million varieties of egg coloring kits, Jello molds (that everyone uses for jello shots, I think) and the enormous array of over priced candy… SHeesh.