This is something I hear with many languages.
I have heard claims that eskimos have XX words for "snow", and that norwegian doesn't have a word for "please".

Well, first of all, "please" isn't a word as such. Sure enough, "please" Is a word, and means about the same as "pleasure". But the way "please" is USED in english, it isn't used as a word, but as an abbreviation of an expression. The full expression (which they use in french) is "s'il vous plaît". Which translates as "if it pleases you", or "could you be so kind".
I don't know about finnish, but in norwegian we have the expression "vær så snill" (technically "be so kind"), which is an abbreviation of "kan du være så snill" ("could you be so kind"). And which is very often shortened into "værsåsnill". And this is the norwegian "word" for "please".

I don't know how many words norwegian have for snow, but if you include words such as "sludd" (sleet) and "hagl" (hail), which are words for various forms of precipitation, as well as words and expressions like "slaps" (slush), "puddersnø" (powder snow) and "skare" (snow crust) which are various words for snow on the ground, then we would easily have dozens of words for snow. And I'm pretty sure english would also have quite a few different words and expressions for snow.

@Tjalve One could say "Olisitko niin kiltti/hyvä" for the "Would you be so kind/good", which is the substitution for the "please", as you state. The "Voisitko" (and many other words with -ko suffix) for "Could you" as mentioned by @Karen also work very well.

Both the number and the definition of "snow" are a stretch, although there are a lot:

http://www.ohmycake-helsinki.com/2013/04/finnish-snow-guide.html
https://www.reddit.com/r/DoesNotTranslate/comments/2qfwmm/finnish_words_for_snow/

Can you actually name 60, EyeOfTheStorm3? I can't find a reference for anything that high.

As for "please":

http://wikitravel.org/en/Finnish_phrasebook

"The word please doesn't translate very easily into Finnish, although starting requests with Saisinko... (Could I please have...) or Voisitko... (Could you please...) can often substitute. If you have been asked something (eg. "What would you like?", or "Where do you want to go?"), you can just state X, kiitos in response. Better yet, just smile! "

@Karen Officially we don't have that many words for the actual snow, but we do have words for what kind of snow it is. Then there's some local dialects that have even more words that describe what the snow is like. If you count all of those 60 is probably pretty low estimate.

The please thing is just like you said. There is no word for it, but we have suffixes that translate to basicly the same thing. Voitko? (can you?) against voisitko (could you?). The latter could be translated to could you please because it's very polite version that is rarely used unless you are trying to be extra polite.

@Barracuda Lumi 1, hanki 2, nietos 3, viti 4, nuoska 5, pyry 6, sohjo 7, loska 8, tykky 9, räntä 10... mmm --- Now what are the other "snow" words?

As for "please" -- we don't like to tell people to please us with whatever it is we want. We just ask if they would do it. Though, there ARE varying degrees with increasing assumption they say no to ask *nicely*, but going too much can be mockery (implying they think too much of themselves usually) -- AND varying degrees to tell people to do stuff. In correct situation, even the "noun, swear-word!" style is appropriate.

Well kinda you can say please. Pyydän saisinko kahvia, for example. It translates "Please, can I get Coffee? If we put please at the end, It would just sound Silly.

In Denmark, it is common to see "venligst", litterally "friendliest" but often better translated "kindly", pressed into service as "please". It even gets placed in the sentence where "please" would go in English, leading to absurdities like "venligst luk døren" in stead of the correct "luk venligst døren" or better "vær venlig at lukke døren", literally "be friendly to close the door."

@Klaus Would you kindly

Danish also have no single word for please. Does any of the Scandinavian languages?

@Carewolf its not direct but we use kindly(snälla) in sweden

@Carewolf Icelandic "vinsamlegast", although you mainly see it written. If someone actually says it they're probably being sarcastic.

@Carewolf The Norwegian "word" "værsåsnill" has exactly the same meaning as "please".
Although "værsåsnill" isn't technically a word. It's a contraction of the words "vær så snill". But it is used as a word. And often also written as a word.
So it seems like it's only Danish, of the Scandinavian languages, that doesn't have a word for "please".

@Tjalve I Danish we have the same in værsgo, short for "vær så god", but is still just a politeness phrase, not quite as universal as please or bitte.