Technically yes, but you shouldn't. Mowing wet grass causes uneven cuts, root tearing, fungal disease spread, and mower damage. Wait 2–4 hours after light rain or 24+ hours after heavy rain.
No — mowing wet grass causes uneven cuts with frayed brown tips, clumping that smothers the lawn, soil compaction from mower wheels on saturated clay, fungal disease spread, and mower deck clogging. In the GTA with its clay-heavy soil, wet mowing leaves ruts that take weeks to level. Wait until the grass blades are dry to the touch and your footprints do not sink into the soil before mowing.
No, in most cases. Morning dew makes grass blades wet enough to cause uneven cutting and fungal spread. Wait until at least 9 am in summer or 10 am in spring and fall, and confirm with the back-of-hand test before starting.
Stop immediately. Light rain on already-dry grass is workable for the first 5 to 10 minutes, but once the grass surface is wet you are wet-mowing. Finish what is safe, park the mower, and resume after the lawn dries.
Those stripes are clumps of wet clippings smothering grass underneath, plus uneven cut quality. Rake or blow the clumps off, water lightly to revive flattened grass, and accept that next mow will look uneven for one cycle.
It can — wet grass clippings lifted by the mower carry weed seeds, especially dandelion seedheads, further across the lawn than dry mowing. Wet conditions also create bare wet-clump-damage patches where new weeds will germinate within 2 weeks.