These items are seen often.  Most often they are either of the "Trigger Finger" version, or the full Extreme Cold Mitten.

These are very useful mittens, but BE AWARE that the untreated leather palms/finger surfaces are NOT water-repellant, and as-issued WILL absorb water like no get out.  If allowed to absorb water, the liners/insulation of the mitts will definitely get wet and lose its' insulating properties.  Might even freeze solid.  NOT GOOD.

I would strongly suggest treating the leather palms/fingers/thumbs with a couple of treatments of good lather-friendly waterproofing, such as offered by Picard.  Other similar, and good leather treatments are also available.  DO NOT use "neetsfoot oil" as it is destructive to leather.  DO NOT use silicone spray as it does not last long.  The fabric portion of the mittens should be treated with modern Durable Water Repellant (DWR), as offered by McNetts and NikWax.

The GI woolen inserts for the trigger finger mittens can be replaced by modern fleece gloves.  Outdoor Research offers such gloves.  Pay attention to sizing when ordering.  Not cheap, but nothing good is cheap.  OR Fleece gloves: https://www.outdoorresearch.com/en/mens/gloves.html?cat=2241&product_highlights=29

If you have GI woolen trigger finger inserts, wash them in cold water and Woolite detergent to prevent shrinkage.

Submitted for your consideration.

Maybe you had the later, much inferior inserts that were mostly made of some sort of fiber that wasn't the original GI wool.  Good deal on having them come out all right, but the downside is whatever you used was junk compared to the early GI 100% wool inserts originally intended.  It's a good point, though, and prospective buyers of such shells ought not count on USGI 100% wool inserts being easily available.  In that case, a couple of pairs of good fleece gloves might do, and Outdoor Research is a good place to start.