They each had a dietary need for roughly 40 lbs of vegetation daily therefore the arctic was not cold when they were thriving there [more likely lush and tropical], but they were all killed in an ice storm of epic proportions."
Those are testable claims which I'm certain have been shown false.
The first obvious observation is: Elephants, rhinoceroses & other large mammals which live in hot climates have minimal hair, and do have other features to shed excess heat -- i.e., large ears.
When remains of similar animals are found in the arctic, they have long hair and smaller ears.
We can see that same long hair today on arctic muskox: 
Second, your claim that mammoths need 40 pounds of vegetation per day, and this is supposedly not available in the arctic, is nonsense when you consider that today's arctic supports half a million caribou in Alaska alone.
So any suggestion that it could not support smaller herds of mammoths is just ludicrous.
Third, climates in ancient times can easily be determined by, among other methods, examining the remains of plants and animals found in geological strata.
If those plants are of species which grow in the tropics then we know the climate was warm, but if they are arctic plants, then we know it was colder.
So here's what we know: for the last several million years, arctic climates have alternated between deep-freeze ice ages of about 100,000 years followed by 10,000 to 20,000 years of warmer "interglacials" such as we have now.
And so far, the earliest woolly mammoth remains date to about 150,000 years ago, and the last about 10,000 years ago.
This time period includes the current plus one previous warm interglacial, with all of the time between being very deep-freeze ice-age climate.
Fourth, the final extinction of woolly mammoths about 10,000 years ago corresponds to warming climate, which caused a 90% reduction in suitable cold-climate mammoth habitat.
As for Dr. Walt Brown's lunacies, I'll have to leave that for someone else to deal with.
Bottom line: any suggestion that artic climates were relatively warm during most of the past ice ages is not supported by any evidence I know of.