There’s no way to really know if she is interested or not except to ask her out again, or simply ask her if she is interested in going out with you. We only have part your relayed conversation, and of course we don’t know anything about either of you.
I personally tend to think she’s probably not interested, based on what your relay as her answer.
If I were truly too busy at the moment, but really interested, I would have said something clear like “I’d love to, but I have too much to do between now and Christmas, how about next weekend?” or something to that effect.
I would want to clearly send the message, “YES” with the caveat that it’s not you it’s the timing.
She didn’t do that.
But, I need to add the disclaimer that she might not have been thinking about her messaging, or she might have been flustered by your invitation, or any number of other “maybe” scenarios. Again, the only way to know is to ask her out again when it’s not holiday time and see what she says.