The felt as you know is designed as a last stand against water intrusion on to the roof sheathing and into the home. Roofing felt or tar paper can be left out in the weather for weeks shedding rain water while the roof is in progress of being completed. The best roofing conditions are of course nice sunny days about 78- 85 degrees but this is not reasonable all year in the vast climates we have in America or with some of our readers all over the world.
The roofing products used on a steep slope roofs { 4:12 or greater } move the moisture downwards to the eaves and off the roof. Both the felt and shingles are designed to be in the wet and rainy conditions. It is a good idea blow off excessive water with a leaf blower in the area you are starting roof and as the day progresses the rest of the felt should dry out. Moisture should evaporate between the shingles and the felt and not cause any issues or damage any of the roofing products.
My concerns with wet or damp felt is that it causes the felt to wrinkle. These wrinkles can hold up the shingles from laying flat till the moisture evaporates. This can be unsightly and disturbing to the home owner. In some cases, I have seen the roofer slice these wrinkles and not repair the felt properly.
So what can you do? Most roofers will use the thicker #30 felts in colder and wet months because they do not wrinkle as much. The new synthetic underlayments are great for not wrinkling but cost a little more. Some roofers try not to tear off more than they can roof in one day to avoid this damp felt. It is also a good idea to cover the felt with a tarp in the area where you are going to first start working in the morning. Again applying the shingles to the damp surface should be ok.
Be advised to check with the manufacturer you are using for best results. One thing to remember low slope roofing {2:12 or less } is totally different. Never work with low slope roofing products when you have damp underlayment or damp wood sheathing is seen. This will trap the moisture and cause blisters when it warms up.
This really did help me understand the wet felt roof . Thanks for making us aware !