This happens when the temperature is coolest often late at night or early in the morning. Few days ago I did night shots and every 4-5 minutes I had to clean filter from water (mist). Is there any (lens safe) facility to stop condensation of moisture on the surface of a lens or a filter, or maybe to slow this process.
The moisture holding capacity of air decreases with decreasing temperature.
Technically, condensation occurs when air with moisture in it is cooled below the point at which the air is able to hold all the moisture that it contains. This is referred to as, not totally surprisingly, the dew point. Very dry air will have a very low dew point. If you can dry the air striking a surface then the surface needs to be very cold relative to the air for condensation to occur.
Theoretically you'd expect that a cold lens introduced into a warm atmosphere would cause condensation, and this is what you see in e.g. tropical butterfly houses when cold cameras meet tropical temperatures. In that case the more enlightened establishments have a warm air blower to heat cameras with on entry. Near instant fix.
In the case of bringing a warm camera into colder air you might expect that the problem would not occur as the warm camera surface would heat the air, increasing its dew point and water carrying capability. Everyone who has taken a warm camera outside on a cold night knows that condensation happens. I looked at several dozen web references on condensation and none adequately explained this effect. Even a USGS school science site did a poor job.
SO there is obviously a complex effect where the combination of energy transfer and air movement results in some of the air falling below its dew point. Experience shows that if temperatures are allowed to equalise the problem vanishes. As equalisation can take several hours, a source of blown air at local ambient temperature is liable to greatly hasten the process.
Here is a typical and excellent example reference on "Cameras, humidity & condensation" where virtually the whole discussion relates to cool equipment in a warm environment.
A clearly explained and elegant explanation of why introducing a camera or other equipment from a warm environment to a cold one results in condensation in an apparently opposite manner to what is expected in theory is given on the site mentioned by @garik on the page Telescope Performance & Cool-Down Vs Dew Heaters. The solution IS a heater, but the reason is worth understanding.
See the above page for details, but in summary
I'd like to apologize for the rough render with poor detail. This answer does not use any magic, but rather chemistry!
Heated UV Protection Filter
The lens warmer uses two two fins, each with a hand warmer rubber banded to it to heat the glass element. The heat from the warmers will quickly get the filter element above ambient temperature, at which point it will no longer condense.
This would be somewhat difficult to physically implement with the tools commonly available. I would consider using a step up ring and a filter larger than necessary. Then glue the aluminum heating plate to the step up ring, and glue (thermal adhesive please!) the filter on top of the plate. A hole has been previously drilled in the plate to allow light to pass.
My early cars without A/C taught me that in cold, avoid breathing out anywhere towards glass that should remain transparent. The escaping air has been warmed up your body and reaching a colder surface will trigger the dew point, just like Russell has described in his answer. Blow air out via a corner of mouth if the important surface (like a windshield, or a lens) is straight in front of you. Photography got me hooked me years later, and even running out to take pictures in 40°C / 70°F below room temperature, I've only experienced the problem of foggy lens when forgetting that simple rule.
When looking specifically for a facility, any device directing breath away from camera, e.g. a curtain or a snorkel, would do. But these are not really necessary, just paying attention will do.
When shooting outside in cold temperatures (or even at dawn when the air temperature is close to the dew point, its the warm air inside the lens that is causing the fog.
The solution is simple if you have some time. Put the lens in an air tight plastic bag (a bread loaf bag works for long lenses), seal it up, and take the lens outside for a couple of hours. Let the lens get down to the outside temperature.
Then you can open up the bag, and shoot happily.
Just remember to put the lens back in the bag when you go back into the heated area, to prevent the warm wet air inside the house from condensing on the cold lens.
What I have found:
1) Answer goes from other field: astronomical observation. Phil was right: it should be some heating device. Here is a sample.
3) Hand-made without heater (maybe it will work): Anti-Dewer: long tube, horn made from cardboard or plastic, it can be covered from the inside with black barhotom (only natural, it is better artificial), and outside paint matt black car paint for better protection from the elements. Get two in one: Anti-Dewer and blend together. Here is a sample.
4) We can use thin sheets of black foam :)