I haven't tested this, but it looks like you need to change:
/common_files/customer/main/register_additional_info.tpl
Code:
{if $v.type eq 'T'}
<input type="text" name="additional_values[{$v.fieldid}]" id="additional_values_{$v.fieldid}" size="32" value="{$v.value|escape}" />
to something like:
Code:
{if $v.type eq 'T'}
<textarea rows="2" cols="20" name="additional_values[{$v.fieldid}]" id="additional_values_{$v.fieldid}">
{$v.value|escape}
</textarea>
I have no idea if this works, or if it has any ill effects otherwise.
Hope that helps,
-Mike