Once ice on the surface of a body of water melts, it can never form again. Particularly at high latitudes, where temperatures are far below freezing for nine months a year.
Down here at 40N, we observe this every year. Lakes and ponds melt every spring, and then never freeze up again. This phenomenon has caused the Colorado Polar Bear population to shrink to dangerously low levels.
The lack of Arctic sea ice did not keep it from snowing in North Dakota and Minnesota today. They are cold places, but snow this early in October is not that common.
If the ice were there, it would have snowed twice as much. Or half as much. Or the same amount.
US Navy arctic ice map is now defunct–
http://www7320.nrlssc.navy.mil/hycomARC/navo/arcticictn_nowcast_anim30d.gif
Not sure what you are referring to. The NIC ice charts are available here:
http://www.natice.noaa.gov/products/
NIC was formerly the Naval Ice Center.