Throughout the ASOIAF universe we have seen numerous examples of a god/gods effecting the story in some way, even if it is through some form of magic/ritual/etc.
For example:
R'hollor: Melisandre/Shadow babies/Deaths: Joffrey/Robb/Balon/Renley/C. Penrose/Resurrection:Beric/Lady Stoneheart/glamours
Old Gods: Weirnet/Bran/COTF/greensight/warging
The Many Faced God of Braavos: Faceless Men/Glamours
There are many other examples that I could list, especially some without direct link to an