To be able to paint your model, you need it to be unwrapped and have a texture assigned to it in the UV/Image Editor.
Your .blend does not have an UV and does not have a texture assigned to it, that’s why you can’t paint it.
As an alternative to painting it you can just give it a material, and change the color that by default is white to a dark brown.
But you should join every single piece of your model together if you don’t want to have to assign that material to the bunch of individual pieces (select all the individual models, press CTRL+J or Object -> Join).
Then once you have added a material (and changed the color to dark brown) , you can then go in Edit Mode, and press P -> “By Loose parts” to un-join all those pieces if you need them to be separate models.
edit : i was slower than usual, i got insta-posted by 2 people