There's also quite a bit of evidence that "the little ice age" was *actually* the natural start of the next/current glacial period, and it was only the arrival of the industrial revolution & rapid increase in fossil-fuel combustion that paused, then slowly reversed, the cooling.
Regardless, "the next ice age" (glaciation) will be nothing like the past, because this time around humans will interfere with it... indirectly, if not directly. Snow gets removed from urban areas & never really gets a foothold anymore. If glaciers come within a hundred miles of Vancouver, Edmonton, Toronto, Montreal, etc, Canada will build nuclear power plants with "cooling" canals like Turkey Point in Miami whose added warmth will stop the glaciers in their tracks (and become very popular with wildlife, who'll ultimately come to depend upon the warm water for their continued existence).
Ditto, for Britain, Scandinavia, and areas near glacier-prone mountains.
Areas like Seattle will start actively melting Mt. Rainier's ice cap to reduce future lahar formation (from instantly-melted ice) during an eruption.
Today, glacier fields are protected & in retreat. Once they start growing instead of shrinking a few hundred years from now (partially neutralized by global warming or not), they won't be left alone to slowly cover North America & Europe the way they did last time. This alone will probably profoundly alter the "ice age's" (glaciation's) course, since we'll be actively disrupting the albedo feedback loop & preventing the development of permafrost in places that are "supposed" to develop it during a cold period.
Put another way, even if we don't try to actively melt glaciers, cities like Edmonton & Glasgow are now several thousand square-kilometer heat islands with black asphalt & actively-plowed roads. If push came to shove, the aforementioned nuclear plants would have their "cooling" canals extended into buried hydronic heat pipes under roads, the surrounding corridor, and entire metro areas if necessary to prevent permafrost & turn plowed snow into meltwater that gets pumped away.