> We're coming out of 1,000 year ice age which means we've, geologically, had an ice age recently.
We (due to climate change) may be coming out of a 2.58 million year ice age (an ice age is a period during which at least one permanent large ice sheet exists; in the case of the current one, it is the Antarctic.)
The last glacial period with the within the current ice age ended 10,000 years ago, so even if you were using “ice age” to refer to a glacial period, we’re not coming out of one of those, either. (The “Little Ice Age”, which you link to the Wikipedia page for, was neither an ice age nor a glacial period, but—as the article you link to notes—a set of regional cool periods at different but close times after the end of the Medieval Warm Period.)
> With continual reduction of greenhouse gases by our growing efforts we could be open to a building of the arctic in the next 500-1000.
Because of the different albedo (ice reflects 50+% percent of solar radiation, sea water around 6%) melting Arctic sea ice will accelerate warming; it's a positive feedback loop; plus, we haven't even started reduction of greenhouse gases, nor have we even achieved reduction in the rate of increase—I think we've managed to decrease the rate of increase of the rate of increase, but that's a far cry from reducing greenhouse gases.)