If I’m picturing this correctly, they have unsecured sliding barn doors that hang from above, but there’s nothing holding them in place below, and there are gaps between the two doors, and maybe also gaps between each door and the barn siding?
The wind load (force) on barn doors can be very powerful-- and when the doors are freely swinging on their hardware, that hardware will fail at some point. I know you want to do something nice, but those gaps that you want to fill are actually serving as a pressure relief valve for the doors. It gives the wind’s energy somewhere to go. Closing the gaps, without doing anything to secure the bottom of the doors, will only increase the strain on the doors and the hardware they hang from.
Even a decrepit old barn can be improved, without it being a major job. (I speak from personal experience, mine dates from late 1800s). For instance, if you’ve got a lot of rot along the bottom of the barn siding, you could tack a length of 2x6" board all allong the bottom. I guarantee you that you can find multiple places along this siding that would hold a fastener. With that new baseboard in place, now you have something you can drill/nail into, anywhere you need to.
But sounds like there’s a lack of tools/tool skills, so I might suggest putting up a wind screen entirely separate from the barn. Stacking roundbales 2-high for the length of the barn would block the prevailing winds and greatly reduce the wind blowing through the barn doors. Straw or corn stover bales are cheaper than hay, and less likely to be eaten. How far away from the barn they need to be depends on the height of the windbreak. Generally a solid barrier like roundbales will create a sheltered zone that extends 10-15x their height. So a line of roundbales stacked 10ft high would shield an area 100-150ft in front it.
