There is a ton of authentic information on Grand Canyon on the park website. I am giving below my experiences which you may not find anywhere else. Enjoy!

If you want to stay on the canyon rim, book well in advance, 6 months in advance. If you want to camp at the Phantom ranch at the bottom of the canyon, book a year in advance.
The North rim is closed in winter so we could only visit the South Rim. December is very cold even on the south rim with snow and ice on the trails. You have to be dressed very warmly to be able to stay outdoors; walk around, unless you want to take the FREE Orange and Blue shuttle rides, get off only at the points to take pictures quickly and get back in the next shuttle. The shuttles ply every 15 minutes.

There are numerous treks that you can do here but we could do only 2 of them.
Trail 1 : Kaibab trail : As we started late in the afternoon, we trekked down till the Ooh aah point which was about 2 miles. The distances may sound short but the trails descend into the canyon and are covered with ice and snow.
Caution : You start off going downhill which relatively takes less effort and energy and one does not realize how far you have reached. The climb up is quite a challenge as you can see from the pictures. On an average a 3 mile round trip would involve a vertical climb of about 1100 feet, which is quite a lot for inexperienced trekkers. Bit of a challenge even for a regular trekker.

Trail 2 : Bright Angel trail : We went till the 3 mile point, which is a 6 mile round trip where you descend 2200 feet and takes 5 – 6 hours. We did it in about 4.5 hours and I would rate it as a difficult trek, especially in winter time where the first half a mile or so is ice and is quite treacherous. As you descend, the temperature rises and by the time you reach the 3 mile mark, you are comfortable. The temperature on the rim was about 6 deg C.

The restaurant at the Bright angel lodge, close to the Bright angel trail head, has good food at reasonable prices and also has a good view of the canyon. Don’t miss!

Next time I would like to do a round trip till the river which is a 16 mile round trip descending 3200 feet although there are warning signs everywhere dissuading you from doing it, scaring
you with consequences such as extreme exhaustion and death if you attempted doing it in 1 day! I met a family who were completing this trip on the day we did the 3 mile trek … so it can be
done with a little preparation.

We stayed at Grand Canyon inn which was a 30 min drive from the south rim. Good rooms, economical.

Caution : If you have parked at the visitor centre, remember that the last shuttle from the trail heads is around 6.45 pm (check the time at the visitor centre). It gets really dark around 5.30 pm in winter and you are totally dependent on the shuttle to get you back to the visitor centre. So keep a watch on the time. Or better still take your car inside which they permit in December.

TIP: If you love nature and like exploring, you have to stay at the canyon for at least 2 nights and devote 2 full days to the sights. I would say that seeing the canyon only from the look-out points is getting only a 10% experience compared to seeing it while trekking down.