When you hear a grinding noise whilst turning, there are a number of things that could be causing the issue. The first thing to do is to try to determine the location of the sound. If the issue occurs only in cold weather, it could be related to your power steering fluid. If the issue only occurs when you're turning one way, but not the other, it might be a CV joint.
Power steering fluid
One very common cause of grinding sounds whilst turning is low power steering fluid. Check the reservoir to see if it's full. If not, be sure to top it up. There are power steering fluids on the market that seal minor leaks in the system. If you're losing fluid (having to replace it more frequently than you change your oil), try one of these before having your car repaired. Cold weather can also be a factor in power steering fluid issues. The fluid becomes more viscous in very cold temperatures, sometimes causing a mild grinding noise. This is an indication that your power steering rack will eventually need to be replaced, as the problem tends to worsen with time.
If the sound only happens when turning one way or the other and makes a very loud grinding noise, this is likely your CV (common velocity) joint. CV joints can degrade when the boot covering them is compromised, allowing moisture and dirt in. If not repaired, a problem with the CV joint could prevent the vehicle from moving. CV joints are more common in front wheel drive cars, but sometimes found on four-wheel drive vehicles as well.
A bad wheel bearing can also cause a grinding sound. If your issue is the wheel bearing, the sound will worsen when you are accelerating and will emanate from near the wheel of the car. A bad wheel bearing will cause the car's steering to feel loose. If your steering seems to have a lot of play and you hear a grinding sound, the problem is likely to be a wheel bearing.
Within the column
If the noise seems to come from the steering column, it's likely an issue with the bearing in the column. Some bearing issues will cause knocking sounds or looseness in the steering wheel itself. A problem like this should be looked at by a mechanic, as is can be quite dangerous, causing the steering wheel to seize up.