An interesting distinction to be made between loving, being in love and falling in love.

Right... which is why I was a little dismayed when I heard the topic was going to be "Falling in Love" ... there's a whole universe of love to write about, and falling in love is just one specific, relatively tiny, corner of it...

So, anyway, in the lines:

On top of Old Smoky, all covered with snow,
I lost my true lover for courting so slow

The speaker had made a promise to wed (or set up an apartment together, if we're gonna be modern about it), but then took so long to follow through on that promise, that the other party gave up and looked somewhere else?

If so, I think s/he made the made the right decision!!