Of course! Fuuko has plenty of warm clothes that Fuuko can change into, so rest assured that Fuuko will be very warm. If Fuuko's raincoat shows up then Fuuko will definitely come wearing that too!

[Since water is going to be involved it makes sense to bring some sort of coat along. Even if they won't actually be getting wet.]

The only water at Fuuko's house will be in the sink or the bathroom, or in the upstairs bedroom if the roof ever falls in again. [...] Fuuko thinks that meeting up somewhere else would be a better idea.