I paint on green felt. I like the results. Below I explain a bit how I do it. I suggest you experiment on very small pieces of felt or canvas or whatever you decide to use until you find the techniques you desire. I have a friend who has used painter drop cloths to make desert mats and those came out great too.
Here is my first mat: link
The water features are plastic sheeting (the kind you put over windows). I cut the felt out where the water is located and then use duck tape and special glues to secure the plastic sheeting to the mat. Then I paint the bottom of the plastic. This makes the water lower than the high ground and adds depth to the mat.
For paints I take dead leaves and a flocked base with no miniatures down to the local hardware store and have their computer color match using the cheapest indoor flats they have. In this way the grass matches my flocking pretty closely.
Do not saturate the felt with paint. Use just enough to color the top. It will soak in a bit but should not bleed through. In this way your felt should remain flexible.
If you use a stiff brush when putting on the grass features, and rub the felt hard when applying the grass paint, and continue to rub when the brush has gone dry, then the felt will fluff up a bit and make it texture a bit like flocking. I actually have had people think I've flocked the felt.
Now the cost of the paints and the plastic sheeting mean I would not save any money if I made just one mat. But I am on number 3 now. They also take me a couple days of work but my friends are very impressed with the results so I'm going to keep doing this.