To keep one's hands warm during the winter, one never needs gloves or mittens.
Premise (after all)
Keeping one’s vital organs warm can keep one’s hands warm as well.
Intermediate Conclusion
One can always keep one’s hands warm simply by putting on an extra layer of clothing, such as a thermal undershirt or a sweater.
Main Conclusion
To keep one’s hands warm during the winter, one never needs gloves or mittens.
Evaluate
There are two arguments here. While the main conclusion seems reasonable given the intermediate conclusion, the intermediate conclusion does not seem to follow from the premise. Because keeping one’s vitals warm can keep one’s hands warm does not mean one will always be able to do so. The intermediate conclusion is much stronger than the premise.