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Padded gloves do throw off your swing / bat "feel". You do now see a lot of guys wearing a little rubber donut thing on the thumb of their top hand. That helps a lot with absorbing the vibration from a mis-hit. It still shivers your hands, but you don't get the piercing pain focused right at the base of your thumb.

[Edit] You do build up some crazy calluses swinging a bat for hours upon hours of practice. They absolutely don't help, like at all, when you strike a ball in on the handle of the bat. It always hurts.