No, actually, Muffin tended to have tonsillitis too easily and I would avoid the rain. I would generally wait until the rain ended. On those days when rain is endless, I understand it can be a problem. Muffin used pads in the garage on rainy days. But I just wouldn't risk her being sick. If we went out when just the grass was wet, she ended up with her legs and tummy completely soaked!
If you have a healthy yorkie that doesn't tend to get tonsillitis or get sick easily, I'd say go for it. Just use an umbrella. Hopefully you have a little raincoat for the little one or at least a sweater or something like that.