I wear my very first nice looking bag that kind of 'drew' me into the world of good quality handbags. It's not designer and I don't really wear it anymore unless it's raining and I need to carry a bag with me. It's made of leather, but it's been through some pretty tough weather and I've applied water protector to it, so it's absolutely fine.
I don't have any coated canvas bags, but I don't wear my Saffiano leather Prada in the rain. It has an open compartment in the middle and it's a taupe color. I don't want to risk getting an unremovable water stain.
i use my Mulberry Alexa as the bag's buffalo leather seems quite hardy. I use Collonil leather gel on it to make it a bit more water resistant and it works. The bag's been through heavy rain and snow with no problems.