In reply to humptydumpty:
"Small icy bit": small icy what? Small icy 30 degree slope? Small icy pitch of grade VI? How small is small? How icy is icy?
On the general question of whether you can winter-walk in trainers with crampons fitted to them, the answer is Yes.
If this is your question, then I'd advise you to buy some flexible walking crampons, fit them to trainers, and test them before you commit to anything worrying.
But I'm not 100% sure from your post if that is what you're asking.