I used to carry both a wind shirt (Patagonia Houdini) and a rain jacket. However, after reading several threads on this forum on this topic, I started leaving the wind shirt behind as an experiment.
I found that so long as I was wearing an appropriate base layer, (Pat R1 hoody + microweight base-layer while snowshoeing, mid-to-lightweight merino top in spring/fall) I was comfortable while moving, and in fact more comfortable because even the best wind shirt inhibits breathability. During stops/around camp, it's no difference whether I throw on my rain jacket or wind shirt, as breathability isn't an issue.
For really chilly/breezy days, a wind shirt might be useful even when moving. For example, while XC skiing in the low 40s, I found myself wishing occasionally for a wind shirt while moving downhill at speed. The wind cut through that R1 and chilled me. But I was never cold or in any danger of hypothermia. And when exerting myself on a climb, the wind shirt would only make me sweat more, and possibly lead to me being colder through evaporative moisture when at rest.
Really, it's up to you. It is only 3-4oz extra. For me, it was a case of BPL causing me to rethink something I had just always done, experiment with an alternative, find the alternative more to my liking, and ending up with one fewer piece of gear in my kit. Which in the end is more appealing on an simplicity level than any noticeable comfort gained from saving 3.5oz.