The set recorded by Steeleye Span (and by Martin Carthy some years earlier) was collected not by them, but by Andy Nisbet (while he was at Swansea University), from "two old ladies in Pembrokeshire".  I think that John P is right to take "Celtic" as being meant very loosely, in this case; indeed, it will have to be if many useful songs are to found.  Largely as a result of marketing exercises, a great many people seem to refer to anything from Ireland or Britain which they like as "Celtic"; this is to misunderstand history and demographics, of course, but there are plenty of people who actually live here who also have rather strange ideas about what it means!  A lot of the time, people are referring to a style more than anything else, which is what I assume is meant here.

The song Kristine was mainly looking for is, as has been pointed out, English, but I don't think that matters; presumably, no one is going to pretend that it isn't!  The peoples of these islands have lived alongside each other for so long that we all have a large body of traditional customs and musics in common; personally I only use the "Celtic" word when referring to Celtic language material; any attempt at a greater distinction is pretty much doomed to failure, and of course interminable argument.

The most useful (available) printed resources have already been mentioned, I think, but there is a great deal of seasonal material in both the DT and Forum; what you might like to try is a search for @carol.  In order to avoid the huge amount of additional hits you'd get from searching the Forum, try going here: Search Results;  de-select the Forum box before running the search.  @wassail and @wren will also get you useful results.  A lot of the files have midis of their tunes, but traditional songs don't come with chords, as a rule, so you may have to work out your own.

To avoid confusion (and arguments), English-language material not from Ireland is probably best described as "British Isles", but I don't expect that it matters much in the circumstances.  It does rankle sometimes when people make "Celtic" records with a large proportion of English material on them, and credit all the countries of origin except England (for which they usually grudgingly substitute "Britain", for some reason) but that's an issue that needn't concern us here.

Have fun, Kristine and friends.  There's a lot of excellent seasonal songs -both religious and secular- to be found (I'm not shooting, Steven!) so long as you don't restrict yourself unnecessarily.