I didn't write a pattern down as I just eyed the work as I went along. But I can tell you roughly what I did. I've never done this before so apologies in advance.
Yarn for hat: Red and white 8 ply acrylic yarn
Yarn for beard: White chunky
Needles: 6mm straight
1. White Brim - A white long rectangle (looks like a little scarf)
CO 20st with 2 white yarns held together. You might need more or less stitches depending on how tall you want the brim. Knit with 2 yarns in garter stitch until the desired length ie stretch it around the helmet where the white brim is meant to sit and knit till it fits very, very tightly around the circumference. Cast off.
3. Red Hat
Using 2 red yarns held together, pick up stitches along the length of your white long rectangle. I picked up one stitch per row. Knit in stocking stitch till the work measures about 15cm. K2G at the start and end of row. Repeat decrease every 4th row until you're left with 10 st. Leave a very long tail and cut yarn. Using a tapestry needle, thread the long tail through every other st on needle and back through remaining stitches. Pull yarn tightly.
4. Finishing hat
Using the long tail, sew the edges together. I used a mattress stitch seam. Make a large white pom pom and attach to the pointy tip of hat. Hat done!
5. Beard - Long white rectangle in loop stitch
CO about 80st with chunky white yarn. Using the loop stitch, knit till desired length. Good instructions for loop sitch here:
CrazyAuntPurl: Loopy is the new crazy!
Knit till desired height for your helmet - measure just below the visor till the bottom edge of helmet. Cast off.
6. Finishing beard
Put the hat onto the helmet and wrap the beard around the front. Sew one end with white yarn onto the Santa hat. Stretch the beard tightly over and sew on the other end. Beard done!
7. Safety features - Non-slip rubber backing
Using non-slip rubber backing that you use under rugs, cut a 5cm strip according to the circumference of your helmet. Seam up end with regular thread or use sewing machine. Now you've got a non-slip "belt". Sew using regular sewing thread to the underside of the white brim on 8 equally spaced out points. Make sure you stretch the hat as you figure out where you need to sew the strip to.
Cut a 15 x 7cm rectangle from the non-slip rubber backing and sew on to the underside of the beard. I sew mine on in the middle top part of the beard ie just under the bottom edge of visor.
Put the Santa hat on to helmet. Fold the pointy red tip to the back of the helmet till it touches the hat and sew in place. This prevents the tip from flying around while you're riding.
That's it! I've tried to explain it as best as I could remember. So if you need further explanation, I'll be glad to clarify. Thanks all!!!