The Upper Yosemite Fall Trail is not closed at the halfway point in the winter. However, it does get much more difficult after Columbia Rock with larger amounts of snow. Finding the trail can be very difficult (if there hasn't been much traffic ahead of you), and snowshoes would help.
However, conditions aren't always the same, and you should absolutely check the weather before hiking this trail in winter, and checking with a ranger on the current conditions of the trail would be a good idea.
Here's the sign we encountered when there was significant snow. As I understand it, there is considerable rockfall and avalanche danger up the trail.