When I first started ice fishing I didn't own an auger. That first winter I used a splitting maul to chop/bust out a hole. I never got wet, but I learned the value of having an acceptable safety margin.
4" is usually quoted as the minimum required for a single person. I have fished on thinner, but I was uncomfortable doing so. This has been a crazy winter, and I would be extremely leery of venturing out, especially since this is your first winter on your pond. There can be weak areas caused by springs, or water movement, or even decaying vegetation on the bottom of the pond. If you do go, I would stick close to shore this winter, don't go alone, and have some safety gear in place. Maybe you should allow yourself some time to become familiar with your new pond's demeanor, and you'll be better prepared for next, hopefully colder, winter.
