White Stag must have gotten complaints about the elasticized fabric "melting" so they came up with a creative warning label! That looks like a rubberized inside waist band, and was useful for keeping a shirt or sweater tucked, and keeping the snow out.
Based purely on the label, these are late 50s or early 60s. For years White Stag used a red label for their sports clothes, then switched to blue (or the red and blue may have been used concurrently) but around 58 or 59, a white label was developed.