I'll have to acknowledge my question might be too vague for a straightforward answer, as can be seen by the various comments. The correct answer, as given by Paul J. Gans, probably is
[V]ery. I know of no way to quantify this.
However, using the comments as a starting point, I read some more around the topic, and I would like to expand on the comments to the question and to summarize what I found out.
Since there's no unit to measure "dangerous" with, we'll first have to get more specific. In the context above, we can offer the following dimensions:
- ease with which LOX + X is set on fire or detonated, the easier, the more dangerous
- predictability of ignition, the less predictable, the more dangerous
- energy output of ignition, the more energy the more dangerous
- speed of reaction, the faster the worse
The core problem with all of the above is that the LOX is not a fuel and will, on its own, do nothing at all. So before we can even speculate on possible reactions, we will have to narrow down the fuel options our spilled LOX might encounter. When we also want to account for oxygen-enriched atmosphere by boiled off LOX, a danger in itself, even without spilled, as matt_black correctly points out, the fuel can be almost anything burnable in the room.
That pretty much takes care of 2), predictability, which is low, so keeping the whole setup safe is difficult. -> Danger: high
Ease of ignition depends on the fuel, and the number we're after is the activation energy (Wikipedia). I found various Internet pages mentioning LOX spill accidents that turned tarmac into an explosive that can be set off by walking or driving over it, although I have not found an actual report of such an accident. So apparently, there are common materials that combine with LOX to a mixture requiring a very low activation energy. -> Danger: high.
Energy content and speed of reaction also depend on the fuel, but the fact that it's being used as rocket propellant and that LOX was used to build explosive charges in mining (so called Oxyliquits (Wikipedia), via permeakra's comment) means that we can expect plenty of both for a number of materials. The article also emphasizes the unpredictability, even of things that are meant to explode. -> Danger: high.
Finally, various safety guidelines inspire vivid imaginations of some scenarios:
The whole floor of an office is known to have caught fire when oxygen vapors contacted a lighted cigarette butt. -- Saftey Precautions for Oxygen Plants
If liquid oxygen spills on asphalt or other surfaces contaminated with combustibles, do not walk on or roll equipment over the area of the spill. Liquid Oxygen, Environmental Health and Safety