Kaeng Krachan

I would suspect there will be a lot of people over the holiday weekend - long weekends usually attract crowds, and this one in particular because, as you know, its the height of the cold/camping season. Before the holiday weekend starts though there should not be many in the weekdays.

But my experience is that they are normally there for the camping and as soon as you go into the forest sections there should not be many people at all.

Agree with Trekker.
I would want to add that I wonder if you will be able to rent a tent that time of year. Yes, normally that is possible, but even though I don't know the number of tents they have at Ban Krang, from what I've seen it is not so many. so you might end up without any tent at all...
Buying a cheap tent in a Tesco Lotus or something might be a wise thing to do.

I just returned from KK yesterday and found it quite chilly in my sleeping bag at Ban Krang. It will certainly get colder. And I would not want to sleep at Panoen Thung... So be prepared. Also, taking a shower this time of the year is not exactly pleasant, haha.

Wildlife can be found throughout the park.
With luck you can see some great wildlife. While I was hiking, finding very recent scrapes with still wet urine drops of leopard, as well as recent tapir dung, my wife drove down the mountain and she got to see a Leopard cross in front of her car at 10:10AM. Surprisingly this was last Sunday when it was very busy and a lot of cars had passed her just before she was lucky to see this big cat.
Too bad I missed it, but well, I will be back ;)

Wish you the best luck!

Honestly I'm not sure if they would have enough sleeping bags. And if you would arrive before the weekend of the 27th December, then I think you should not have any problem to rent the gear (even the tents). But if you're arriving in the weekend, I'm not sure. I would not want to risk it ;)
I don't know much about car rental in the area. I would guess Hua Hin should have some rental companies.
Make sure to rent something with high clearance and a bit rugged, a pick-up truck would do. 4x4 is not really necessary, at least not in the dry season, but the road is not good enough to drive with a normal sedan or something like that.
Another option is to ask at the visitor centre (which is near the Kaeng Krachan Dam) for a car with driver. From what I've heard a full day should be 1800 baht. But I guess you really need to inform the driver why you're there for. Most of them race to the viewpoint and back down, and don't look for wildlife along the roads.

I just checked on google and found huahincarrental.com and they have pick-ups for 1000 baht per day if you rent for 1 up to 6 days. Longer periods the price will drop.
And a 4x4 Toyota Vigo costs 1100 baht per day.
BTW I don't have any experience with this company, it is just what google found for me :)

Enjoy your time!