Creeping Mulberries

Can anyone tell me the right way to prune a weeping mulberry? It all looks like a bowl of spaghetti. I got in there last summer and took out the middle most offending branches so my grandsons had a great fort. Now it's all bare of leaves, and I wonder if I should thin it. Another in my neighborhood looks like it hasn't ever been trimmed or thinned, and it is big and healthy in the summer.
Help appreciated.
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