Well it kind of depends upon your time-frame.
Evergreens like the Balsam Fir that makes up most of the Christmas Trees produced will lower your PH levels some, but depending upon what you are growing, that could be good or bad. The real problem is not what the trees are made of, it is that they are freshly cut.
The problem with freshly cut
wood is that as it decays, it actually robs the soil of nitrogen in order for the breakdown of its cellular structure to happen. But this only happens for a few years, after that, as the breakdown is in full swing, it goes the other way and gives off that nitrogen thus feeding your plants. This is both good and bad. Because you are using fresh cut wood, it takes longer for the released nitrogen to happen, but your hugelkultur stays intact longer. The preferred method is actually to use decayed wood because the breakdown is already happening and thus you will get nitrogen into your plantings sooner. However, you are also going to have to renew your hugelkultur sooner.
The great thing about Christmas trees...fir especially is that it is not rot resistant at all. In fact it is one of the first woods to rot in the forest, so in a hugelkultur, if you must use fresh cut wood, Christmas trees would be your best choice.