Even an old wooden box that is large enough to fit the boots can be turned into a boot storage box by the addition of a door on hinges. Tuck the boots inside this cupboard each time after use and the spiders won't be able to crawl inside.
 The mudroom, laundry or a spare cupboard near the back door can all work as suitable places for storing boots when not in use and thereby reducing the chances of spiders living inside.
Purchase or make a small cupboard with a door that shuts properly.
Make a special indoor place to keep boots.
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