To change the thumbnail, you have to update the workshop item from within Besiege.
If you do so, you have the option to change the thumbnail of your item right when choosing the tags, just click on the preview image on the left.

A folder containing thumbnail images will now open. Before you delete the automatically generated thumbnail, make sure the one you want to use has a .png or .jpg format (other formats might work too, I'm not sure) and the size does not exceed 1MB.
Delete the old thumbnail and rename the image you want to use so it has the exact same file name like the automatically generated thumbnail, move the image file to the thumbnail folder.

Now go back to Besiege, click the red X and restart the upload/update process, the item should now show the thumbnail you want to use in the preview on the left - do not forget to choose tags (and of course, click "update" and choose the item you wish to be affected).