Your statement of "was wondering if the significance of this trend can be calculated by simply correlating the linear trend with the actual data" is wrong. Without getting into technical details, suffice to say that correlation is a way to see how close your two compared samples are to having a linear fit between them, but says nothing about how likely you are to observe that relationship given a null hypothesis (in this case, the null would be that there is no relationship). Correlation is just a number that tells you the relationship between two samples, but that's it (for example, the correlation between two samples with sample size 3 and sample size 100000 can be the same, but you'd expect that the larger samples to have higher validity in any statistical testing.
I'm not sure what you're looking for, but the absolute simplest thing would be to do a linear regression where you predict wind speed given the dates (organize them so that the earliest month/year date is 1, and then second month is 2, third is 3, and the first month of the next year is 1+12 = 13, etc). Once you calculate the coefficient for effect of date on wind speed, called $\hat{\beta}$ just do a simple t-test.
Alternatively, what about a linear regression where you predict wind speed given time, and maybe include month fixed effects, and then run a t-test to see if the coefficient for time is statistically significant? This would basically amount to saying: "after controlling for the fact that different months may have different wind speeds different from the effect of this time change, what is the linear effect of time on wind speed, and is it statistically different from 0?"
Dunno what your preferred analysis software is, but in R, this would amount to having a dataset (dataframe or datatable) where each row is an observation and include columns for dates (ie month/year variable), month (dec,jan,feb), and wind speed. Then you'd write:
reg <- lm(formula = wind_speed ~ dates + month, data = dataset)
And R will compute the t-test for you, which you can view using summary(reg).
Hope this helps!
