The brst part of a winter visit is the shuttle isn't running. You can drive your car up to the top, rather than eaiting in line for shuttle at visitor center.
The park is open all winter. While St George has a mild winter, it does snow on occasion and Zion NP has several areas at high altitude, so there is a risk of not being able to access a given trail or area. But it's also very quiet off-season, so there is that...
Yes it is ipen all 24/7 all year
There is horse back riding and I believe it's open all year.
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