Is it appropriate to bring coffee and cookies to a PhD defense? First of all, I've already asked my adviser about this, but I just want to see what is the overall idea of the community on this.

In Mexico it is usually required for the student to do this, but that is about the only place I have references of people doing defenses.

I was thinking of bringing bottled water, but since is the middle of the winter I thought coffee might be a better choice.
How I have seen it handle in France: usually, no food and drinks is given out during the defense, except for a bottle of water and a glass who are set on table of each member of the defense committee. However, as you say, it may be cold outside and committee members may be glad for a hot drink and/or maybe something to eat (depending what time it is). So, it is quite customary for the thesis advisor(s) to actually invite the committee members to join him some time before the defense starts, where they can make small talk and drink coffee. If the defense starts early afternoon, they committee can even go to lunch together, giving them an opportunity to discuss practical stuff (who will chair the committee? what order will people talk in? etc.).

Then, after the defense is concluded, there is a celebratory “cocktail” (buffet and drinks) to which the defense committee is invited, and to which they usually attend at least for half an hour.