Glaciers actually do retreat and advance seasonally or on even longer cycles. Some have terminuses that move back and forth literal miles. One of the key indicators of climate change is the fact that globally, glaciers are retreating more than they’re advancing on average.
It’s not impossible to invade the US. It’s been done several times already, for example 1942 and 1812. Mexico, which shares the same oceanic borders, was invaded by France in 1861 and of course the entirety of the Americas was essentially invaded by colonial settlers.
It’s unlikely for other reasons, but nothing about it is impossible.