For a winter wedding/Christmas wedding/nature-themed wedding you could decorate disks of tree trunk with pine needle clusters and red berries (holly berries or plastic) with a nice ribbon. If you can find a birch that is already down or you can find one that needs trimming, this would be very eco-friendly and responsible as well.
You can always use another kind of wood if birch is not available. Some wood has a strong smell and some does not. If yours does not and you want some, add a drop of essential oil to the wood to make it smell nice.