Why do membrane proteins at lower temperatures contain more alpha helices than beta sheets?
The reason could be the greater motility of the alpha helix, compared with the more rigid beta sheet.
This allows the enzyme to remain functional at low temperature.
The proteins of such organisms tend also to have less hydrophobic regions and covalent bonds.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1692995/pdf/12171655.pdf
Molecular basis of cold adaptation
Salvino D’Amico, Paule Claverie, Tony Collins, Daphne´ Georlette,
Emmanuelle Gratia, Anne Hoyoux, Marie-Alice Meuwis, Georges Feller
and Charles Gerday*

This doesn't refer to alpha helix explicitly, however alpha helix are known to allow more flexibility than beta sheets, so it's reasonable to argue that the increase in alpha helix could be one of several strategies used to obtain more flexible enzymes, as well as other means cited in the paper.

This point is also made by Brock-Biology of microorganisms(2015) pag.161


  Several cold-active enzymes whose structure is known show a
  greater content of α-helix and lesser content of β-sheet secondary
  structure ( Section 4.14) than do enzymes that show little
  or no activity in the cold. Because β-sheet secondary structures
  tend to be more rigid than α-helices, the greater α-helix content of cold-active enzymes allows these proteins greater flexibility
  for catalyzing their reactions at cold temperatures.


However unfortunately no reference is provided about this claim.