Actually, in later tmux versions (I am seeing this on 1.9a), it looks like there's been a change in the way styles are set.
While @ChrisJohnsen's answer still applies (and my tmuxconfig certainly still uses these statements) the new way to do this as explained by the manage is to use
*-style rather than the triplet of
*-fg, so you can specify the style for such a window option with a single statement rather than three.
Set status line message command style, where style is a
comma-separated list of characteristics to be specified.
These may be `bg=colour' to set the background colour,
`fg=colour' to set the foreground colour, and a list of
attributes as specified below.
The colour is one of: black, red, green, yellow, blue,
magenta, cyan, white, aixterm bright variants (if sup-
ported: brightred, brightgreen, and so on), colour0 to
colour255 from the 256-colour set, default, or a hexadec-
imal RGB string such as `#ffffff', which chooses the
closest match from the default 256-colour set.
The attributes is either none or a comma-delimited list
of one or more of: bright (or bold), dim, underscore,
blink, reverse, hidden, or italics, to turn an attribute
on, or an attribute prefixed with `no' to turn one off.
With the -a flag to the set-option command the new style
is added otherwise the existing style is replaced.
So this declaration would then be:
set-option -gw window-status-activity-style fg=red,bg=black,bold