Mrthfx

We've found all sorts of interesting stuff in arctic ice & permafrost around the world.

Bacteria & the like far older than the more media friendly mammoth specimens have been found, living bacteria has been found in ice cores as old as 420,000 years.

Obviously I'm not thinking about living specimens.

The ebb & flow of the ice & permafrost through our various ice ages are probably a factor in what might plausibly have survived unthawed to be found & by extension where (not all dinosaurs lived exclusively in warm climates) & when any particular species was found.

So is a frozen dinosaur in any way plausible, how about a neanderthal?

Permanent ice caps have not been a constant during Earth history. For example we know that in the past the poles were free from ice.

Therefore the oldest possible frozen sample is as old as the oldest permanent ice caps or frozen terrain on Earth. Anything that got frozen before that time has been thawed in the meantime.

We have the actual example of the Ice Man -- beaker culture neolithic discovered in the Alps. He was about 9000 years old.

So that can set some parameters:

Hunter or band traveling across and icefield that is in a pocket between multiple peaks. Dies in late fall. Exceptional snowfall period, so is buried under permanent snow cover which as the ice builds up puts him deeper.

Because it's a basin, the ice there doesn't move. When the ice builds up in thickness, there is a shear plane above it. Can't have glaciers feeding into the bowl either. So take a bowl that is surrounded by steep peaks that can avalanche into the bowl, but not form glaciers. Eventually the ice gets thick enough that it is above the bowl, and the excess flows off.

I think the Columbia Icefield on the border between Alberta and BC fits these criteria.

To me this would be a plausible event going back to the start of the last ice age. This would get you back to somewhere between 115,000 and 22,000 years ago.
Last Glacial Period -- Wikipedia For the longer period, you need to have some glaciation through the short inter-glacials. A mountain based shield would meet this requirement.

If you want a story line, "My father's father said that he knew a hunter who had crossed The Pass of the Winds." But in the hundred years since the cooling climate has created a permanent snowfield there.

Much of Antarctica is under water. Strip off the ice, and you have substantial inland seas. Antarctica without ice You could have various things trapped by glaciers closing off the openings. I don't know to what extent these levels freeze down. If there were hollows above the then present sea level you could trap land animals as described above. This could plausibly take you back to the beginning of the Antarctic ice cap something like 40 Megayear ago. I suspect that the timing of that is vague, so you might plausibly extend it back some. Dig into Antarctic paleo climate.

The oldest frozen specimens would likely be roughly 15-30 million years old and would be whatever critters were on Antarctica during the Oligocene or early Miocene.

Around that time, Antarctica finished its split from other land masses with the opening of the Drake Passage between it and South America, allowing the Antarctic Circumpolar Current to begin keeping warmer waters away and permanently freezing the continent into what we know today.

Until it fully froze, conifer forests and steppes covered the continent, and if Antarctic fauna were anything like the rest of the world it was dominated by a mix of critters that were vaguely similar to today's large mammals, rodents, and sea life.

So, it looks like your frozen Oligocene Park will probably be decorated with odd-looking pine trees, and be filled with horses and mice with weird snouts. Not as awe-inspiring as a T-Rex, but still pretty cool.

As for finding frozen Neanderthals, it's possible but unlikely. In order to be found frozen, they would have needed to die in an area of permafrost that has been unchanged for the last 40-50,000 years, and their known range doesn't have many options for that. However, we did find a 5,000 year old mummy frozen in the Alps, so anything's possible.

a study published this week (October 10 [2012]) in the Proceedings of the Royal Society B estimates that DNA from bone has a half-life of 521 years

(Link)

That's the rate the DNA molecules spontaneously fall apart. This study does not address DNA in tissue other than bone, or how freezing temperature affects the deterioration of DNA, but I think it's still a decent estimate to start from.

How good is your technology at reconstructing DNA from teeny fragments in trillions of cells? Neaderthals went extinct 35,000 years ago. After that long (~67 half life periods) only 1/147573950000000000000th of the DNA will be left. The article sets 1.5 million years as the point after which DNA strands are too short to be read, but the point at which you can no longer recreate the whole genome might be much shorter than that.

It is an extreme long shot but it might be possible, some day. The extreme desiccating effects of amber has been shown to preserve DNA, even in specimens of the right time period. And at least one fragment of a dinosaur flesh has been found preserved in amber. Several feathers are also known to exist.

The problems are three fold, not every piece of amber preserves DNA in fact most do not, and dinosaur material in amber are extremely rare, even by normal amber preservation standards. Lastly the DNA is extremely fragmentary so you are talking about massive reconstruction, to the point that said organism would be more invented than restored. It would also be the single largest and most complex genomic reconstruction in history, to the point you really would need a much better understanding of genomics and biochemistry than we have now. The only thing you have working for you is phylogenetic bracketing, and the fact said dinosaurs would be closely related to the ancestors of birds.