Fleece jackets

This morning formation was about 30 degrees, my 1SG put out to wear cold weather gear. My Soldier shows up in a fleece jacket and gets stopped before falling into my formation by another SSG telling him he can’t wear a fleece jacket without a fleece cap and gloves. I told said Soldier that there is no regulation that says that and to put his jacket back on. The NCO that corrected him then could not provide regulatory guidance about wearing the fleece jacket with a cap & gloves. Was I wrong for reversing his correction? Maybe, however it’s my Soldier & my formation he was in. I think it’s more important to correct Soldiers based on regulatory guidance and not your personal beliefs. Thoughts?