Sorry, have no idea if any private visit can be organized. Please contact thru' mail for the same.

You do not need to pre plan to see the Temple of Love- you will however need a full access pass, which is a few dollars/euros more. If you scheduled a tour in the afternoon, you will want to skip the palace tour and head to the gardens...once outside, stay to your right and follow signs to the Tridant, it is a pretty 10-15 minute walk. Once at the trident, you can see Mary Antoinettes petite house, farm, etc. It is stunning. The pathway sort of follows around and the Temple is near the exit. Plan well, so you do not miss your tour. I recommend getting to Versailles at 9 or 10 am. Let me know if you have further questions

Agree, it is stunning. I have been in the winter, just dress appropriately and you will be fine

The Temple of Love is part of the Estate of Trianon which, in the low season (1-Nov to 31-Mar) is open everyday except Mondays from noon to 5:30 pm as per their website. The ticket office closing at 4:50 pm and last admission at 5:00 pm. It is also closed on Christmas and New Year. However it is an outdoor feature and end of December is going to be very cold in Versailles. Also, the sun will probably set before the closing time. So plan accordingly. If in doubt about specific dates, it is always best to check with the palace.

I can't remember the exact location of the Temple of Love. If it's in the estate of Marly it's currently from 7:30 to 21:30 every day at the moment for the summer season. The park itself is from 7 to 20:00.

The entire to the temple is free of cost