Yes this is doable via CSS, but remember a post can be in mutiple categories so the last category mentioned in the CSS Insert will be dominant. Here is a samle of what you would put in the ATO->Add HTML/CSS Inserts->CSS Inserts - this first part will take care of the post titles
HTML Code:
.category-announcements .post-headline h1,
.category-announcements .post-headline h2 a {color:red !important;}
.category-events .post-headline h1,
.category-events .post-headline h2 a {color: blue !important;}
.category-frogs .post-headline h1,
.category-frogs .post-headline h2 a {color: green !important;}
this second part will take care of teh category names in the category widget. You will have to match the item number with the correct category. The easy way to figure it out is to add the category widget to your page, view the page then look at the soruce of the page.
HTML Code:
.cat-item-3 a {color:red !important;}
.cat-item-35 a {color: blue !important;}
.cat-item-7 a {color: green !important;}
You can use this as a guide for the post footers
HTML Code:
.category-announcements .post-footer a,
.category-announcements .post-footer {color:red !important;}
.category-events .post-footer a,
.category-events .post-footer {color: blue !important;}
.category-frogs .post-footer a,
.category-frogs .post-footer {color: green !important;}