According to the current food lists, spaghetti squash is the only winter squash allowed in phase 1. You can add other winter squashes back in phase 2, but they count as starches (like breads and grains) and are therefore limited.
You can tell summer squash from winter squash by looking at the skin/rind. If the skin is very thin and easy to peel or cut, it's a summer squash. If it's hard to cut into or peel, it's probably a winter squash.