Yes, you can definitely do this in Magento.
Create new header template and place it under, lets say: page/html/checkout-header.phtml
.
All you have to do to use this header template on checkout page is add following layout update to your theme's local.xml
<checkout_onepage_index>
<reference name="header">
<action method="setTemplate"><value>page/html/checkout-header.phtml</value></action>
</reference>
</checkout_onepage_index>
To change footer template, simply reference footer
instead of header
. In case you'd like to update header or footer templates on some other page than checkout, simply change checkout_onepage_index
to coorect layout handle for that page (checkout_cart_index
for cart, for example).
Best of luck,