Depends on your kid
I think the solution depends entirely on your kid. They develop at such different rates at that age that you can't make a general statement. However, the good news is that you should easily be able to find something that will work.
If your daughter is of average or better size or strength then she will probably be able to handle a youth full faced helmet fine. My younger son is about average size / strength and started with an HJC full face at that age with no problems. We have a nephew that struggled with the same helmet at the same age. My suggestion is have your daughter try on a full size helmet. Have her quickly move her head around and see if she has any trouble controlling the weight. If not, you're probably fine for the trail. If not, one of the open face helmets will work. (The HJC helmets have worked out great for my kids. They adjust well and have held up to the rough and tumble my boys put them through.)
Once you've got the helmet sorted out the next biggest thing for success is to make sure she's warm and comfortable. Make sure she's got really good mittens and boots. Kids have a lot less body mass and can get cold much faster. They tend to do ok when they are out playing in the snow because they generate their own heat but just sitting on the sled and riding in the wind chill can cool them off quickly. They also don't tend to notice or say anything until they are really cold. Nothing ruins a ride with your kid faster then them having aching cold hands or feet when you're a 20 minute ride from the nearest place to warm up.
My suggestion is to get really warm mittens with the heat packet pockets in them, and then have a warm pair of gloves as a backup. Adjust based on the outside temps.
Please don't let this deter you from getting out there. Both my sons love sledding. My 9 year old rides his Yammi Bravo on our property or doubles up with us on the trail rides. My 12 year old just passed the safety course last weekend and is looking forward to riding his new (to us) '96 Indy Lite project sled in a couple of weeks. They've been riding since they were 4 and 7 respectively. Love to see kids getting into our sport!