Davidfpo posted Denmark was not involved in the opening
Steve’s question has been bugging me, so I have done a bit of digging around my e-files. As far as I can find, I was completely wrong suggesting that Denmark may have contributed SOF forces (possibly the conflation of my fallible memory - Denmark contributed to 200 SOF to OEF in 2002). David is right that Denmark was not involved in the opening.

But it was a 'member' of the invading coalition.

The Danish parliament on 21 March 2003 passed resolution nr. B 118, which furnished parliamentary consent for the contribution of Danish military forces to the ‘multinational effort’ (this resolution was notable as reportedly it was the first time since 1864 that Denmark was a ‘warring nation’). The Danish contribution was one corvette and one submarine. Given how late in the day the resolution was passed, the corvette did not get on station until 9th April when it joined the US-UK-Aus operations; reportedly it was deployed in the northern area of the Gulf. I found nothing on precisely when the submarine arrived or what it did, only a vague statement that it was ‘deployed in the area’ (the Gulf?) and so seemingly would have arrived in the Gulf (if it was not there already) before the corvette.

So it seems officially Denmark was one of the five members of the US-led coalition that invaded Iraq, but only furnished two ships, no ground forces, and did not participate in the initial phases of the invasion (hence, as an answer to Steve's latest question, were not part of the initial entry force, unless there were Danish SOF forces surreptitiously involved - but again, I did not find anything saying there were)

The only stuff in my files I found on the Czech Republic was that it was undecided whether to side with the US-UK or France-Germany on the issue. That that newly elected president Vaclav Klaus was against the war, as was Czech public opinion, suggests that is is very unlikely that the Czech Republic was a member of the invading coalition (but I may stand to be corrected on this last point).