i was just recently researching this topic myself
there are some pretty good articles on this and yeeeees a whoooole bunch of science exlaining how lakes/water freezes over.
after reading quite a few articles...it all comes down to - it freezes when it feezes
There are simply soooo many factors that you can't really tell if its safe or not just by doing some math, science, checking weather...
basically what it comes down to is - you gotta know the lake. What do the locals say how it freezes? there are some lakes where it takes only couple of days before it freezes and its ok to kite on (I live close to Neusiedler see in Austria) or it might take at least a good week of well below zero before a lake is safe to ride on.
major factors are how deep the lake is, plants in the lake, some lakes might have warmer spring or bubbles which form because of...who knows why.
Right opposite to my house,e.g. is a tiny pond. Can't be deeper than 10-15feet yet it still didnt freeze over and Neusiedlersee is flozen solid since days (and I was kiting there 2 days ago)! I suppose its because of some plants / rotting going on in the pond which prevents it from freezing.
You simply just can't know for sure and the best way is to look out for locals to get out there and skate...
general rules are that ice is OK to walk/skate/SNK on when its 4-5inches thick. For this...i suppose you just have to drill a whole obviously you'd want to check at least couple spots starting pretty close to the shore going out farther (right at the shore the lake just doesnt freeze at all/lightly btw).
You can find some charts based on science calculations which show graphs how fast ice forms on ....NORMAL lakes (ie no under-currents, springs, rotting vegetation underneath). Google it FYI but in reality....it kind of doesnt mean much bc your life does depend on more factors than just some science graphs.
ow an last point - wind does chill and helps to freeze the lake MUCH faster than if no wind! It simply takes off the heat from the lake faster. Snow cover, on the other hand, acts as "insulator" and makes the ice grow MUCH slower (2x slower I read) than if no-snow. Lake also freezes from the shore to the middle - so in theory the ice is weakest in the middle of the lake.