I can confirm from personal experience that cold push up BG levels as your body/liver release extra glucose to fight the lurgy.
Unfortunately, I find illness pushes up BG and high BG exaggerates any illness so it becomes a double-edged sword.
If you can take corrective bolus doses to keep your BG down, this should help ... and reduce your sickness time.
I usually increase my basal to compensate but, if you do this, take care not to over compensate.
Thankfully, I am not able to suffer from anything as bad as manflu.
I hope you get better soon.