The answer to this will differ from newspaper to newspaper and from issue to issue. Unless we were to undertake a detailed analysis of every letter to the editor, there is no way to answer this in an objective and factual way. In addition, it is not always clear that facts could be used in a given letter.
For example, let us look at the letters to the editor in the New York Times link below. There are three letters on the issue of whether people who go to church are healthier than those who do not. In the first letter, there are no facts offered. For example, the writer talks about what “faith and liturgy should” do. That is an opinion, not a fact. In the second letter, some facts are offered. However, some opinions are offered as well. Here, the author is trying to discuss some methodological reasons why the conclusions about church and health might need to be examined more closely. Finally, the third letter asserts facts but does not actually prove them. The author says that the evidence in the original article “comes from studies that are seriously flawed” but he does not prove this. Therefore, it is not clear if we should treat this as a fact or an opinion. The author is stating it as a fact, but does not prove it.
In short, there is no way to objectively answer this question. My feeling is that most letters to the editor that I read are based more on opinion than on fact, but this is not the result of an objective and comprehensive study.