Hi Daniella,

I don't know specifically about AudioMoth, but people have had very good results reducing or eliminating wind noice on things like GoPros or iPhones, etc. using simple Microphone Windscreen foam.  You can buy ones for headsets and the like pretty cheap (10 for $1 for the little ones).  You can just cut them up and either tape them in place on the inside of the case or rubber band them on the outside.  

Also, if the sounds you are trying to extract are still audible, but hard to pull out of the noise, you might also be able to post-process the wind noise out.  Wind tends to be heavy in low frequencies, so depending on what you are looking for you might be able to just filter the lower frequencies out, or use an open source tool like Audacity.  But if your signal is buried deep within the noise, these tools might also corrupt your target signal.

Hope this helps.

Drue

I second what Drue said on both fronts. Using a windscreen for any microphone is really helpful in reducing wind interference. For the Audiomoth's size, you could probably use a lavalier mic windscreen of some sort inside your case. I post-process wind interference out sometimes using bandpass filters in RavenPro (cutting out low frequencies <1kHz usually gets most of it at the site I work at) but this will depend on the frequencies of your target sounds. 

furry "dead cat" covers and blimps work best for cutting down wind noise, and a very good spectral noise repair tool, though it's paid, iZotope RX8. There is a de-wind module, but you can also teach it what to repair. I believe Davinci Resolve and Adobe Audition might also have wind reduction tools, but my go-to is iZotope RX8.