One major idea behind medieval nominalism is that universals are not entities but concepts or general names (lat. nomina) that we use to pick out certain features of particulars.
I am in favour of the medieval approach
I see universals such as "red", "hot" and "north" as concepts which tie together the common properties of particulars, which are then named. So "north" becomes the concept which means closest to the north pole (of a magnet or of the Earth). I can't get my head round how north could be an entity in any other manner than a concept which describes a spacial relation or a rule for help in navigating. It may then acquire other meanings in language, but the first people to use the term north must have used it as a rule to describe that spacial relation, or perhaps to point to a particular place that is north of another place.
I have been trying to imagine a world without any people, to think through what implications that might have on my opinion about particulars and universals. In such a world I think we would still have particulars, but I'm not sure if we would have universals. As soon as we bring sentient beings into the world I think they must create universals, which implies to me that they must be man made.
However, picking up on Armstrong's view about scientific laws, I then thought that perhaps I am wrong! In a world without people we would still have "gravity" as a universal law, and so I switched back to thinking that universals are things which are, quite literally "universal". This may sound naive, it certainly does as I type it.
My only conclusion is that we can probably define "universal" to mean whatever we want. Since it is not an object we can point at, no-one can truly (or perhaps helpfully) say "No, your wrong, you don't actually mean what you just said".
From my previous course, I came down on the side of believing that there is some form of contradiction when we reject a universal law. Whether this contradiction is imposed by our understanding (Kant) or by our language (Wittgenstein) or is innate, I'm not sure. Perhaps it is all three.
I want to come down on the side of a simplistic approach, and say that universals apply to universal "things" such as either laws of nature, or concepts which apply everywhere and at every time (such as north, red, hot and even horse).
I like Armstrong's focus on truth-makers, but I think this allows for a large number of universals.
Whether these universals are man-made or "in" nature is still up for grabs. Hume would argue that we can never know whether they are "in" nature, and it does seem to be that you have to have an omniscient point of view in order to know the truth. This becomes an epistemological question.
From a metaphysical standpoint I want to say that universals exist as concepts, but I'm not sure whether we can say more about their ontological status.