I have discovered that if you use the 1 3 7 & 9 on your number keypad you can go diagonally. Also if you hold down 2 arrow keys you can go diagonally and sometimes when you hold the cursor over the spot diagonally you'll travel that way.
Well don't feel like the lone ranger....I started some of it yesterday and it seems like it took me forever to even get into the adventures, that ice is tricky. Maybe someone else knows a better way and will share it with us.
Edit: If you go to Mette's page you will find a solution to 'diagonal' coutesy of Popo.