Check this out: https://www.esri.com/arcgis-blog/products/product/analytics/displaying-speed-and-direction-symbology-from-u-and-v-vectors/
I think this answers your questions, but note that you can also display raster wind data as point wind barbs. Met data often come in raster U & V components (speed east, speed north - negative values go the opposite direction), and ArcMap (and ArcGIS Pro) can symbolize the rasters as points. This isn't really what you're asking, so I won't go into detail, but if you start with a raster, you don't need to convert it into points.
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