The roads on this 500km trip are pretty good with smooth tarmac and hardly any broken patches, so your car will not be put through any major torture. However, remember that these are narrow roads with a lot of traffic. Plus there are chances of rain around Dhanaulti and snow and ice around Harsil. Your car's tyres need to be in immaculate condition and there has to be an experienced driver at the wheel.
At Harsil, the gearstick may feel a little stiff but don't worry - the cold causes the oil to thicken. Start your car and let it idle for around five minutes before you begin driving.
The defogger in your car can be a boon as the rear windshield ices up rapidly when it is snowing. Also check that the air-conditioning vent system is working well because you might need to direct the draft towards the front windscreen to prevent it from fogging up from inside.
Pack in woollens, walking shoes and torches. An umbrella or a raincoat is also necessary, else you might be stuck in your tent even when there is a slight drizzle.
Camera batteries will not last long in the cold climate, so throw in an extra pair. If you have rechargeable batteries, it's a good idea to carry a device with which you can charge the batteries, using your car's cigarette lighter as electricity in these places plays hide and seek and the voltage constantly fluctuates.
Harsil, because of its proximity to the holy town of Gangotri, is a dry area and there is no liquor on sale here.

The highway from Delhi to Dehradun is quite chaotic with plenty of two-wheeler and tractor traffic. When the sugarcane harvest season is on (around May and June) there are a number of animal carts carrying the harvest to the sugar mills, and they cause a lot of hold-ups on the road.
Remember that the Muzzafarnagar bypass is very smooth and convenient but do try and avoid traversing it after dark. There have been incidents of robbery on this lonely road. Also keep in mind that it is not wise to halt and give anybody a lift on this part of the route.
Once you're past Dehradun and Mussourie, the road narrows down sharply and there are no safety barriers on the edge. Drive very cautiously and sound the horn at every corner.
The road from Uttarkashi to Harsil is an imposing one, surrounded as it is by high rocky mountains and the Bhagirathi river that flows alongside the road. There are plenty of blind corners here too and the roads are at times very slippery due to rain.
Pine forests abound in the area and pine needles lying on the road can prove very dangerous and the car could skid under sharp braking.