To make your snowflakes have sides that look like branches for a simple miniature snowflake tree, you can cut your pattern similar to the one shown in the photo on this page. Experiment, you may find other patterns you like for your particular style of trees, any snowflake will work for making the trees, and they don't need to all be the same.
Start the Cuts With V's
To begin cutting branched stars or snowflakes cut two v's at the wide end of your folded paper as shown above. The distance you leave from the edge of the V to the fold of your snowflake edge, will be half the width of each branch.
Once you have the two V's cut on the outer edge of the snowflake, work down each side, cutting free another branchlet angled to match the side of the V, I kept my branchlets even with the other side, but you can make them alternate if you wish.
Cutting the Center Hole For the Snowflake Tree Trunk
To cut the hole for the tree trunk to pass through, clip a very small piece off the narrow pointed end of your folded paper. Don't make this a very large cut. If you do get too large a hole you can patch it closed wih a scrap of paper set under the hole and then trim a new one.
Open your snowflakes / stars carefully. You can press them flat with a dry iron on a low setting if you wish.