Some German pilsner beers have and "ice-cold filtered" ("eiskalt gefiltert") line on their bottle labels. Is there any difference (regarding the taste first of all) between "normal" filtering and the ice-cold filtering of beer?
It suggests that the filtering is somehow better. But really it's Marketing - conjuring the mental image of a delicious cold frosty beer.
The base idea is that proteins & yeasts in the beer (which cause haze) will clump together because of the cold - with the implication that somehow this provides better filtering.
The truth of it is that no beer is filtered at non-cold temperatures.
Filtering can make a very "bright" beer - that is, it is clear. Filtering is done with different technologies, and down to different levels. Some beer styles are not filtered at all (e.g. German Hefeweizens - cloudy wheat beers) as are many craft beers, whereas others are filtered to the point where just about all particulates - including yeasts and suspended proteins are removed.
Traditionally, lagered beers had a long time for the yeast etc. to settle out, thus producing an quite bright beer without filtering. Many home brewers use this technique too.
Filtering can remove a lot of flavour from the beverage, but it does increase shelf-stability and product longevity.
From a home-brewing point of view: cold-crashing is when you take your fermenting/ed wort and stick it in the refrigerator causing the yeast to become inactive and/or fall out of solution. It can be used as a way to quickly stop fermentation if a desired ABV (% alcohol) has been reached. However, the more common reason this is done is to bring clarity to the beer more quickly. The even less common answer is fractional freezing to increase the ABV.
99/100 times the answer is cold-crashing/chill-filtering is a way to bring clarity to the beer. As the beer brews and yeast becomes inactive, it falls out of solution to the bottom (there is a difference on where fermentation occurs in ales v lagers) forming a "trub." Even if you let the beer set in a still, sterile environment for months... you can still get more yeast to fall out of solution by bringing the temperature down a considerable amount. There are definitely times that you don't want this to happen as the yeast strains also impart flavors to beers. The "banana esters" you get (or that some perceive) from Belgian beers actually comes from the yeast that remain in the beer. Here is a quick run down of identifying yeast flavors and what you should anticipate tasting in some styles. Here is a neat info-graphic from brew-dog that talks about yeast in the brewing process, how some strains impart flavors, and what the options are for "finishing" your beer.
Stopping the fermentation too soon can leave unwanted flavors in your beer. The one that immediately comes to mind is Diacetyl. This PDF is an explanation of the timeline for the creation of Diacetyl in the fermenting process. They tend to produce butter flavors but are considered undesirable in higher concentration by BJCP (beer judge certification program). Here is a list of 15 common off-flavors, their sources, and how they affect beers.
Fractional freezing is not a filtration method. It is being included because we're talking about making beer cold before we're packaging it. Because beer yeast can't survive in concentrations >14% ABV... Making it so cold the water freezes and can be removed before the alcohol portion freezes is a way to concentrate and jack-up the %ABV. Here is a link from PopSci talking about fractional freezing more in depth.
All of this just to say - Chill filtering has a time and a place in beers depending on what you want the end result of your brew to be. The real reason anyone touts a process in advertising is just to help differentiate themselves from the competition. Miller Lite always advertises "Triple Hops Brewed" like it is innovative. Really, adding hops at the beginning of the brew impart bitterness, middle of the brew is some bitter more flavor, end is almost purely for aromatic purposes. A lot of beers you have will have been brewed with hops placed into the the process at three different times.
Fun link for hop-type-flavor-characteristics in beers.