Well, I'm still working a bit in the dark because I don't know what your input looks like, I don't know what output you are trying to produce, and I don't know what the context is at the entry point. But let's try anyway...
<xsl:call-template name="actorTotal">
<xsl:with-param name="node" select="ownedMember"/>
<xsl:with-param name="actorCount" select="0"/>
<xsl:with-param name="memberCount" select="count(ownedMember)"/>
</xsl:call-template>
From this we know that "node" is a set of zero or more nodes, which are siblings to each other: your choice of variable name suggests that there is exactly one node, but on the other hand the presence of memberCount suggests there might be several.
Now we see:
<xsl:if test="$memberCount !=0">
<xsl:choose>
<xsl:when test="@xsi:type='uml:Actor'">
<xsl:call-template name="actorTotal">
<xsl:with-param name="node" select="$node/following-sibling::*[1]"/>
Firstly, referring to @xsi:type accesses an attribute of the context node, which is passed to named templates as an implicit parameter. Did you intend this? I've no idea what the context node is, so I can't tell, but I suspect you meant $node/@xsi:type.
Secondly, if $node can contain several nodes, then "$node/following-sibling::*[1]" is going to select several nodes, which doesn't seem like a good idea.
Anyway, your code looks like an attempt at a classic head-tail recursion (of which there are plenty of examples in my book, incidentally). When the sequence you are processing using head-tail recursion is a sequence of siblings, you have two choices: you can pass a single node $node, and then use $node to refer to the head and use $node/following-sibling::* to access the tail of the sequence, or you can pass the whole sequence as $nodes, in which case you must use $nodes[1] to access the head and $nodes[position()!=1] to refer to the tail. You seem to be mixing the two approaches: you are passing the whole sequence, but then you are referring to $node as if you had only passed a single node.
Finally, from what I can see, your code is simply trying to count the number of nodes with @xsi:type='uml:actor'. If that's all you need to do, then you're making it far too difficult: it's just select="count(ownedMember[@xsi:type='uml:actor'])".
Michael Kay
http://www.saxonica.com/
Author, XSLT Programmer's Reference and XPath 2.0 Programmer's Reference