Palaeolithic people lived in cold climates, but not arctic. Remember that in over 500,000 years of history, there were changes in climate. They had to adapt to Ice Ages, especially the last great one. In fact, the Mesolithic, a transitional period between the Neolithic and the Palaeolithic, is the period when the ice caps are receeding and food sources/availability are changing... the stone technology that defines "palaeolithic" then changes to meet the new needs, and thus we have the "mesolithic" which means the "stone age in between" (TMI...sorry)
There have been no palaeolithic finds in the British Isles (well, that is debated, but I won't go into it), but mainland Europe, yes. Even in the northern reaches of the continent. Africa, Russia (but southern & in mountainous regions), China, SE Asia, South Asia (Himalaya foothills and in the hills of SW India, but probably the entire subcontinent), Indonesia and of course the Near East (predominantly along the Levantine coast, but that is just where the vast majority of archaeological exploration has taken place, so that may be co-incidental.) In Europe -- Greece, the Balkans, France, Italy, Switzerland, Austria, Hungary, Germany. I think Scandanavia too, but I may be wrong. Think regions with mountains with caves, a lot of water sources, good natural supplies of meat and plants (not desertic), and ways to travel (i.e. valleys or low mountain passes...) between regions.
What would seasonal eating look like in snow bound areas? Meat, I think. OR they would have moved south as the food became more restricted. Both options are viable, depending on location. We see both in the archaeological record, but migrations of specific individuals is not reconstructable in the archaeological record, so it is just a theory.
The Neanderthal question: yes there are two theories about the Neanderthal demise. (I told you I was simplifying...) Assimilation or extinction. There are DNA studies going on right now, and that will help answer that question. The answer may be BOTH happened (in some regions assimilation, in some extinction), but this will be big news once the DNA explorations are finished. I'm very interested for the results. I personally think that the strong regionalism of the palaeolithic period may be the foundation for genetic variation in things like blood type, skin/hair/eye color, some genetic conditions, etc.
I want to stress something: while the neolithic brought to us dairy and readily available grains/legums, only the DAIRY is a new introduction. People were eating the grains and legumes seasonally (i.e. not all the time, and in great variety) so I don't personally think eating some grains/beans/rice is a bad thing or in deviation from a good palaeo based diet. It is the dairy that I see as a particular problem. But not necessarily in children (unless they show allergic symptoms)...of course, a long nursing relationship of mom's milk is the absolute best. But as adult palaeolithic people, we would've lost our source of milk for good, and that is why our ability to generate the enzymes to process it go away. There might be a small variation in who produces enzymes by where your ancestry is from, but the enzymes are made for you to ingest MOM'S milk, not cows milk -- they are very different nutritionally -- human milk = higher in sugar; cow's milk = lower in sugar, higher in protein. I can't remember the differences in detail, but it is obvious that cow's milk has different stuff...it grows baby cows into several hundred lb large animals in little over a year. We grow babies, maybe, 20-25 lbs in a year... Cow milk is based on one food, grass (ideally) -- our milk is enriched and formed by omnivorous eating. You get the point.... our body digests mom's milk just fine, but cow's milk is, well, a whole 'nother beast. I want to add here that I think the NT goes a long way to HELPING us digest milk...it adds bacteria to the food that does SOME of what our body can't. So sure, small quantities of kefir, yogurt, cottage cheese, etc. might be just fine. Small quantities.
How do you get calcium without it? Green foods, fish (small fish w/bones) like sardines --- consumed in fairly large quantities in many traditional societies, nuts & seeds (sesame seed are a great source.) I take a cal/mag supplement (a whole food based one) and give one to my children. Can't hurt since we don't eat dairy (I seem to have a pretty serious allergy, my son is showing symptoms, my husband seems to tolerate it OK, and my daughter is on the boob-juice.)
Rice -- rice isn't an strong allergy source. Rice is a variation of GRASS and is low in protein. I wouldn't worry too much about rice in your diet (brown rice = less of a glycemic index, and if you are worried about blood sugar, you should eat it in moderation)... I personally don't feel that rice is something you have to give up on the palaeo diet. It is a wild growing plant in Asia and was used by palaeo peoples there before cultivation. It was probably the earliest cultivated food (there is debate on this...I won't go into it.)
OK...I have to shower. I'm enjoying the discussion. I'm gonna post a recipe (no dairy) that I made last night that was yummy in a separate entry to this thread.