Hot glue won't bond with the wood and will peel and the glue in the material will gum it up and make it stiff where you put it. Work with no seams if you don't sew and staple the material to the chair with a staple gun or decorative tacks. You didn't show a picture of the chair so I don't know what you are trying to do. It is not impossible but I wouldn't want to ruin my chair and material with the hot glue.
Unless you have a cordless glue gun, the cords on the other ones only reach so far, which means you would have to work quite close to an outlet. Another thing if you use the hot glue, anytime you have to press the fabric onto the hot glue you are apt to get burned fingers. In my experience the cold glue doesn't stick real well.
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