A druid was a someone of a similar position to a priest in Celtic Britain since that religion has reduced in size quite significantly the term has been adapted to cover a practitioner of the Celtic faith.
It's difficult to say much about the original druids as they didn't leave any written texts themselves so we only really have documents from Roman Britain which aren't particularly focused on the Celtic faith obviously. From there original holy places though we can see that they did often conduct ceremonies outside and held a high degree of symbolism that could easily be attributed to nature so the assumption is yes. Certainly druidic practices today hold the natural world in high regard and honor the harvest it brings. So modern druids yes, original druids probably.
I'd also like to point out that not everyone who follows a Celtic pantheon considers themselves a druid. As well, not all modern day druids follow a Celtic pantheon. While that is probably the norm, it's not always the case; for example - in the druid organization ADF, one can follow any of the Indo-European pantheons.
If you're interested in modern day druid practices, I suggest checking out the ADF or OBOD websites, as well as druidnetwork.org.
That leads onto a debate I've had many times about a difference between Druid and Neo-Pagan Druid. Neo-Pagan Druid is a whole host of polytheistic religions borrowing some aspects of druidism where as many who consider themselves a "true Druid" attempt to take all the druidic practices (although this is often not the case even for what we know to be true of druidism as there are many Roman records of druid human sacrifice which is obviously not practiced in either religion). Personally I see little difference between the two and assumed that those that called themselves a druid would be glad of the extra numbers which most of them appear to be but some of the more "traditional" practitioners from my home town appear to see it as a "dilution of their beliefs", even though what they practice is already a considerable dilution from the original.
I personally consider myself to be Celtic but shun the title of Druid simply because I do not observe nature in the same way as is described in the few remaining Celtic texts we have left. Druids are supposed to be able to divine past, present and future from nothing but watching animals go about their daily business which I personally make no real attempts to do. It is this core belief from druidism that appears to have given rise to the ecological aspect of the religion which in turn gave rise to neo-pagan movement of it.