First question is 'Where in Derbyshire?' I must admit I associate nailmaking with Staffordshire - and with women and children toiling unhealthily in back yards! [I am descended from 'lady nailmakers' - but not on the Howarth side.] The reason that I ask is that in the nineteenth century a very high proportion of Howarths were in the textile trades, and some of these were carried on in north Derbyshire (eg New Mills). If your ancestors were in those parts, I would think that there is quite a high probability that their origins are Lancashire not Yorkshire.
If your family tradition is that your family are from Yorkshire, and is soundly based, then there are two possibilities. The first (but probably least likely) is that you are descended from indigenous Yorkshire people. There is a parish of Haworth (probably a World Heritage Centre by now and certaily a tourist mega-magnet on account of Charlotte Bronte). There will undoubtedly be some Haworths who took their name from that location and/or others in Yorkshire (eg there is a Hewarth). The second is that your people are only in Yorkshire in transit, coming 'originally' - in the sense of 'in the thirteenth century at the time surnames were adopted' from the estate called Howarth in Rochdale. The weight of numbers is with Lancashire.
The DNA project has demonstrated that most but not all Lancashire Howarths (all spellings) and some from Yorkshire in the Hebden Bridge / Elland area are descended from a single progenitor. The DNA project results obtained so far (although the numbers involved to date are small) do support the historic tradition/assumtion that the great majority of Howarths - who for the most part can trace back to Eastern Lancashire - are members of this clan. There are project members who do not fit this pattern, which may be because of illegitimacy (quite a small proportion over time) or simply indicate that they originate in other locations with names like Howarth - for instance there is a place called Hewath Bridge in Garstang in Lancashire and a possibility that one of our project memebrs whose ancestors come from that location have a separate legitimate line.
You can follow up what I have summarised here in more detail if you go to the project website at www.worldfamilies.net/surnames/haworth and click on Newletter. I did also prepare a paper on the origins and distribution of the name, which I have failed to get onto the website in user friendly format (there are tables showing surname distribution which simply will not open). I shall be happy to send you a copy if you give me your email address - I do not see that I can attach it to this message.
If - as I hope - you are curious about the DNA project and what it can tell you about your Howarth origins - and in particular the possibility that it will help to establish whether you are a member of the main grop - then the way to do this is to join the project, and you will see instructions about how to do this on the website. [In caseof difficulty do not hesitate to contact me for guidance.] As you probably realise a yDNA project depends upon DNA samples provided by Howarth males (since only the males inherit the y-chromosome). For you to participate it would therefore be necessary for you to persuade a brother, father, uncle, cousin etc - a Howarth with a direct male descent - to provide the yDNA sample on which the process depends. We do as it happens have a number of instances where it is a female Howarth who is interested in family history, and has persuaded a male relation to provide the sample. I treat them as equal members and share all inform ation with both: it seems to work well.
So there we are. I hope that this provides an adequate initial answer to you query and that I shall be hearing further from you as a project participant - and as I say shall be happy to send you a copy of my note on surname distribution and spellings (though I must admit that it was not written with Derbyshire in mind).