Wow. This song has so much promise but you really need to spend more time on the lyric structure. Sadly, it's all over the place - and I say this with the utmost respect because I feel you have a good song here.!
You have no rhyme scheme here which stops the song from flowing as it should. I know there are those who feel that a writer should not be tied to rhyming schemes as it limits them somewhat. But i'm completely in the other camp on this one - and so are the vast majority of the greatest writers of the last century.
With a little effort this could be so easily fixed. an ABCB rhyme scheme would seem to work:
Christmas Eve by a fireplace
Watching softly falling SNOW : This should be the rhyme line in each verse.
In this yuletide memory with my love tonight
Wassail’s brewing on the stove:: use the "meet me by the mistletoe" line here to rhyme with SNOW
Christmas carols on the radio
Twinkling lights on the tree:: Change this line to rhyme with mistletoe.
In this yuletide memory be my love tonight
Meet me by the mistletoe
Christmas time can be romantic
There’s a magic in the AIR:: Again, this would be your easiest rhyme line
All alone just the two of us
Let’s make a memory ...."That only we can SHARE" just a thought lol.

A Christmas memory
We don’t have to go out anywhere
You can stay right here with me:: change this line to rhyme with "mistletoe"
In this yuletide memory be my love tonight
Meet me by the mistletoe
Solo
Christmas time can be romantic
There’s a magic in the air
All alone just the two of us
Let’s make a memory
A Christmas memory
Don’t need presents, don’t need anything
All I want is here with me :: again, change to rhyme with mistletoe.
You will be my everything be my love tonight
Meet me by the mistletoe
Make a Christmas memory
Be my love tonight
Meet me by the mistletoe
There are plenty of rhymes to choose from: Blow, Glow, Aglow, To and Fro, Show, Snow.
This is said constructively and with respect and of course you are free to ignore me entirely.

Good luck with the song.