When does the law of diminishing returns apply? Law of diminishing returns does not always apply:

The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower incremental per-unit returns.

I interpret "productive process" as a process that creates a product other than money.

Many productive processes can be done in parallel.

I see how it is true for any process with a central control, because that is limited by the interaction with the instances, so at some point adding a new instance requires additional changes.

But A productive process does not need to be centrally controlled.

If I run a snowball factory, I can add more workers, invest in required infrastructure like gloves, and send them out to build snowballs autonomously.

The central work does not only scale linearly, it even scales constant! The total effort summed up over all instances scales  linearly.

To be strict, it scales exactly linearly because adding a later instance can not add less productivity than an earlier, because the earlier instances are not in communication with the central point at the time. The first instance does not differ from any other, because their creation does not differ. 

If I would insist to earn money, the money transport is limited in  bandwidth. We have freight trains, that's good enough. But there is also a limit in snowball to money conversion by market interaction, as a market is finite.

So, producing money is limited final market size, there can be a snowball I can not sell. Adding instances does not increase production of money.

But the production of snowballs seems to be limited only by the availability of snow and homo sapiens - by climate change.

What's wrong with that? 

Of course, "law" does not mean it strictly applies always. Is it that I just constructed an example outside its validity? Where is it valid, if that is well defined? Or is the argument above wrong?
Law of diminishing returns refers to profits or benefit per unit of output. This will inevitably decline, profits are defined as total revenue minus costs $\pi=TR-TC$ are thought to be increasing with production but at declining rate, this can be both due to the revenue and cost part.

Costs can in principle be increasing, constant or decreasing with scale. In the first case one source of diminishing returns would be already increasing costs. In the latter case we need to examine the revenue part, but note that most economists think that even if some businesses have constant or decreasing costs along a large part of cost curve these should eventually start increasing as eventually the demand of firm for inputs would be so great to lead to higher and higher increases in the price of those inputs. If you already hired all snow collectors you need to start hiring doctors, programmers etc. to pick snow. So at some point every cost curve should be increasing due to scarcity of inputs.

Now when it comes to the total revenue part that will also be increasing in quantity but at declining rate. The reason for this is that the market price of your good is not set in stone. Increase supply and the price will drop. All people have declining marginal utility of consumption so at some point if you supply too many units to the market the price will drop. Even if you would have constant costs or decreasing costs over the whole cost curve eventually the negative change of price due to larger quantity will be larger than any cost reduction due to decreasing costs.

So in short the law of diminishing returns for firms works both because the more you consume of something the less you desire it so demand is downward sloping and because costs should increase with production at some point along the cost curve.