Yes cookies are browser specific.
And the size determined by "size" and "cols" attributes (in <input/> and <textarea/> respectively) varies a lot between browsers. CSS can sort that out, but .. well ... the forum does have one or two, er, coding anomolies about it
I use Phoenix (moz1.3b) almost exclusively now; at first the narrow textarea bothered me, but you get used to it. It's a small thing compared with using a browser that supports string-matching attribute selectors