Options for powering Winter Holiday Train
If you want to “turn on and forget” you might want to look into obtaining a circle of old 9V track (metal rails produced by LEGO until 2007) and a power supply, plus a 9V train motor. It will not be cheap (the track pieces, especially curves, won’t be too expensive but a working 9V train motor is a $50-$75 purchase) however it will allow you to turn the train on and keep it running.

(Image copied from this thread which will be useful to troubleshoot if you have issues with your 9V setup).
FOLLOW-UP: After writing this answer, I realized I too need a circle of 9V track for my Christmas tree train :). I went ahead and bought an incomplete but working 9V train set on EBay for $100, which gives me the transformer, power cord, power supply, a 9V motor and some track. I then added the missing pieces of track from BrickLink (&lt;$1 per curve, $4-$5 for straight, plus shipping) and was all done for less than $150, with extra pieces from the incomplete set such as wheel sets, magnetic couplers and the sunken train bases which are quite valuable nowadays. If you compare that with buying the retired rechargeable battery box and all the PF components, that is similar money, with the downside for PF that you still need to charge every so often - which is what I used to do. One watch-out: these 9V tracks were made both in Dark Gray as well as in Dark Bluish Gray, so expect color differences if you try to mix and match these. I don’t mind as I intend to ballast my tracks anyways, and color differences make for a more “natural” look.