The general instructions for "Large Snowman Mittens" are the same as the smaller version, with these exceptions:
Cast on 40
Work 18-22 rounds of ribbing (the photo mitten has 22...if that's too much cuff for your taste, cut it down)
After ribbing, divide the stitches 20-10-10 on the needles.
Begin the graph immediately after the ribbing (no plain stockinette rows)
Mark the thumb placement on Round 14 of the chart.
Mark 7 stitches for the thumb.
At end of graph, begin the top-of-hand decreases as for the smaller mittens.
Thumb: worked over 15 stitches. Work 14 rounds even, then decrease top of thumb as for the smaller mittens.
Download the Large Snowman graph here