I've just made my first lager, it is currently lagering at 1 C. What is happening to my beer at this temperature? Is the yeast still active? And most importantly: What is happening at this temperature that would not at higher temperatures?
Lagering temp adjustments are done gradually not like a cold crash.
Lager yeast strains are very much alive and active during lagering. The colder temps slow the yeast metabolism, they are struggling to survive, the byproduct is they consume phenols and other things they made or ignored during primary.
Story Time - here's a little illustration, you're in the snow near freezing starving and have no energy and are near death the only thing available to eat is the grease soaked paper wrapper from the burger you had 2 weeks ago in your pocket, you bet you eat it. But If you have the energy to prepare or search for easier food you won't. This is basically the situation lagering puts yeast in.
1°C - The lower the temp, the slower the yeast are to clean up. 1°C is the usually a temperature for a several month lagering. Raise temp to reduce lagering time at the trade off of quality. Low and slow is the way for quality.
The primary thing that is happening is that stuff is dropping clear. The cold temp in combination with sitting still for extended time allows even the smallest of insoluble particles settle out of the beer.
Secondary may be some yeast activity, but its very slow. I have made plenty of lagers and much of the yeast work is done before you do the lager phase. When fermented right many lagers taste great even without the lager phase. I have often gone right to serving a lager just 6 weeks into the process and those beers went into the lager phase. That's not to say the beers would be even better with an extended lager phase.
In theory a good lager ferment doesn't leave much 'clean up' for the yeast to do. If a diacetyl rest was performed then the higher temp encouraged the yeast clean up thing to happen then, before lager phase.
So ultimately at 1C for a month its all my first point, clarity. Keep in mind that with clarity the dropping yeast pull with it certain flavor compounds.
Your beer is developing the clean crisp flavour profile associated with lagers.
The yeast is still active, this is one of the main distingushing factors of a lager yeast is it doesn't beome dormat at low temps but continues to ferment, even if slowly. Still any sudden drops will cause dormancy.
The main thing happening to your beer is the break down of sulphur compunds(H2S), lager yeast tends to produce more sulphur off flavours than other yeasts, but during lagering cleans these up. Some other off flavours are also broken down.
Also as already mentioned it allows the beer to drop clear.
Regarding time to lager 3-4 weeks at 3C should provide time for the clean up to occur once primary fermentation has reached 1-2 points off final gravity and you have done your diacetyl rest.
You don't have to leave it for months, but this can depend on the strain of yeast used and the higher the OG the longer the lager, so with a 1065 OG you may leave it 3 months, and some yeasts produce far more sulphur compounds than others and require longer to remove them from the beer.