When we speak of the moisture in the air we refer to "humidity". When we wish to express the amount of moisture contained in the air, we generally will use the term relative humidity.
Relative humidity is the percentage of moisture contained in the air compared to the amount the air could hold if it were filled to 100% saturation. There is a catch though - the amount of moisture air can hold is dependent upon the temperature and pressure of the air (since, in most common environments, air temperature will usually play a larger role than air pressure, we will only be discussing the effects of air temperature on relative humidity).
As air temperature falls, its ability to contain moisture lessens. So the colder the air becomes, the less moisture it can hold. This is one reason places with extreme cold like Antarctica receive very little snow fall.
As the temperature of air rises, so does its ability to hold moisture. Think of how muggy it can feel after a brief rain shower on a hot, humid summer day - the evaporating rain quickly raises the humidity in the warm air. A very simple analogy might be:
Imagine cold air as a 1 gallon bucket. If we place 1 quart of water into this bucket, it will be holding 25% of its capacity. We would say the relative humidity is at 25%.
Now imagine hot air as a 4 gallon bucket. If we place 4 quarts of water into this bucket, it will be holding 25% of its capacity as well. Relative humidity would still be at 25%.
The "cold air" bucket was at 25% capacity with only 1 quart, while the "hot air" bucket was also at 25% capacity even though it was hold 4 times as much water. This is because the "hot air" bucket had a larger holding capacity.
Using this bucket analogy, if our usual relative humidity levels are about 60% that would mean the "cold air" bucket is containing almost 2 1/2 quarts of water - while the "hot air" bucket would be containing a little more that 9 1/2 quarts of water. Of course relative humidity is not measured by the bucket.
So even though winter air may be at 70% relative humidity it will obviously be holding much less actual moisture than a hot summer day at 70% relative humidity.
If you have ever looked closely at a weather report you will notice that relative humidity is constantly fluctuating depending on, among other factors, current temperature. Below is an example of a clear August day in Maine,
Notice how the relative humidity begins around 100% in the morning (about the time of dew fall) and then drops through the day as temperatures clime until about 5pm when it reaches its low of about 50%, and then begins to climb again. While this cyclical action is pretty common each day in summer, the relative humidity levels of course differ.
To add to this, in the cold of winter, we close our homes tight and turn up our sources of heat. Unless humidity is introduced in some form, our indoor humidity levels drop quite a bit. In common heating systems fresh (cold air with its low humidity) is brought into the home and heated. While the actual amount of moisture in the air remains close to the same, the now hot air has a much greater moisture holding ability (its relative humidity will now be quit low). This very low relative humidity can cause us to experience dry skin, coughing, sore throats (among other problems). Low relative humidity can cause many problems when it comes to our pianos and other furniture.