Some places have very consistent winds that last for a season. That is why most people ride from North to South if they do the Pacific Coast trail in OR and CA. Our tailwinds last summer were endless, loved it and had great sympathy for the few riders we saw coming from the South. If I was stuck in a place like that here there was no hope that the winds would every change, I would shorten my daily goals to have a more manageable trip - that assumes you have the time available to do so instead of having to be back at work by a fixed date.
If you are in the middle of a large land mass, like North America, you might be able to plan your daily schedule better for the wind. Usually wind strongest about 1pm or 2pm, steadily weakens after 4pm and is quite weak between sunup and about 10am. A friend of mine crossed the country and they often were on the road in the dark in the morning to avoid the heat, finished the daily ride well before noon, you could do that to avoid some of the wind.
Since you posted this question, you have internet access. WUnderground has a good graphical display of the 10 day forecast, it includes wind direction and speed on their graph. Plus of course the forecast for precipitation is nice to have too. This link is the forecast for my home area, you would have to type in your anticipated location in a few days to get a good forecast. I usually trust the forecast to be pretty good out about six days, beyond that it starts getting to be a bit more like gambling. This could help plan which days you want to ride and which ones you don't want to ride, and if you might have a tailwind coming later.
Madison, Wisconsin (53719) Conditions & Forecast | Weather Underground
I regularly use my drop bars in head winds, that is why I have drop bars. I have done a couple bike tours in Europe where the tour group provided hybrid bikes for us to ride. Where the pavement was smooth and little chance that I would have to suddenly veer around something, I occasionally rested my forearms on the flat bars and steered that way to get a bit more aero position when the winds were strong.
Since I am on the topic of weather forecasts, a couple other links that I often looked at when on a long tour to get an estimate of what the weather might be like in a week or two:
Climate Prediction Center - 6 to 10 Day Outlook
Climate Prediction Center - 8 to 14 Day Outlook