Type of hunting matters regarding type of clothing, but keeping those young ones both warm and dry at that age is the ticket to a good experience that will keep them coming back for more. Especially for those early experiences, dont make it a suck fest... there is time enough for that as they get older

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To that end, a couple points/suggestions that I found worked well (some may not be as critical in certain locales).
1. Kids grow fast, unless you have a lot of money to spare, dont feel the need to track down high end hunting gear. At that age, you won't be enduring any serious weather and they will outgrow it every year anyway.
2. For any active hunting (i.e. small game), avoid cotton. Polypropylene or other synthetics work well and can be found in kids sizes. High performance wool in kids sizes is very niche and honestly not needed.
3. Boots/shoes always suck for small kids, that will be a limiting factor for them no matter what unless they are in tennis shoes. Get something that will keep their feet dry, use tennis shoes when you are able. Don't walk them to the point of hotspots/blisters....
4. Thrift stores are a great place to check out. Facebook marketplace for used kids stuff too. You won't find an all matching "outfit", but you dont need that anyway. The majority of my kids hunting clothing is from thrift stores for pennies on the dollar.
5. Always have gloves and multiple pairs with you. I dont knownof any gortex/waterproof kids gloves. Regardless, They will find a way to get their hands wet on a sunny dry day and you are on a short timer before they are all done unless you throw on a fresh pair.
6. Bring hand and foot warmers. Those sleeves you can stick your hands in are pretty universal sized and are awesome. Kids can last 10x longer if their fingers and toes stay warm.
7. Don't get caught up over male vs female hunting clothes, it doesn't matter. Marketing plays that game for sales. An extra small in "womans" jacket may size just right for your young one so try them out too. Performance and function matters, labels dont.
Mostly obvious points, but hope this helps!