Mumford and Sons 'Winter Winds' song meaning

"Winter Winds" as written by Winston Aubrey Aladar Marshall, Edward James Milton Dwane, Benjamin Walter David Lovett and Marcus Oliver Johnstone Mumford

As the winter winds litter London with lonely hearts
Oh the warmth in your eyes swept me into your arms
Was it love or fear of the cold that led us through the night?
For every kiss your beauty trumped my doubt

And my head told my heart
Let love grow
But my heart told my head
This time no
This time no

We'll be washed and buried one day my girl
And the time we were given will be left for the world
The flesh that lived and loved will be eaten by plague
So let the memories be good for those who stay

And my head told my heart
Let love grow
But my heart told my head
This time no
Yes, my heart told my head
This time no
This time no

Oh the shame that sent me off from the God that I once loved
Was the same that sent me into your arms
Oh and pestilence is won when you are lost and I am gone
And no hope, no hope will overcome

But if your strife strikes at your sleep
Remember spring swaps snow for leaves
You'll be happy and wholesome again
When the city clears and sun ascends

And my head told my heart
Let love grow
But my heart told my head
This time no

And my head told my heart
Let love grow
But my heart told my head
This time no
This time no

meaning of song lyric:

if you've ever been in the situation where you were single, and not because of your own personal choice, for a long time, this song really resonates. You're ashamed and disappointed in yourself, and feel like you're a failure for not being in a relationship. The winter is when I feel it most of all, because during the other seasons you meet people and have fun with new people and try out relationships that do or do not work out, but in the winter you're stuck with what you found or did not find, ad relationships formed in the summer crumble around then too. No one wants to bring someone home for Christmas they just met. So the winter is rough for singles waiting for valentine's day and other holidays to start trying the dating scene again. Hence the very first line.

When you're in the situation that you feel desperate just to love and be loved, you tend to snatch up the first chance to date you can, and it usually turns out poorly. Hence the next three lines where the narrator expresses doubt that the relationship is founded upon mutual love and respect versus that desperation. 

The chorus really confirms this in that it's all a mind game when you're in a relationship because you don't want to be single but are with the wrong person. You form no meaningful connections with them (hence the heart saying no) but you want to be anything but single (so you try to convince yourself to love them and make it last, hence your head trying to force your heart to say yes).

The shame that sent the narrator off from the god he once loved is the shame of being alone. It doesn't make sense for shame about cheating to drive someone to cheat. The narrator felt alone and ashamed, and left Christianity after a crisis of faith. When you want things to go your way and your faith fails you, sometimes you feel alone enough in belief to leave your religion. That shame of being alone led the narrator to pursue an unhappy relationship.

The second stanza starting with 'washed and buried' is the narrator advising the girl to do what makes her happy, not implying it be with him.

The fourth stanza starting with "if your strife" is the narrator advising her not to be worried about being dissatisfied with the relationship, and that things will clear up for her and she'll find someone who values her as herself in a relationship, not so much someone desperate for a relationship in itself. It could also be interpreted as the narrator talking to himself, and that he should let things go, stop fretting (letting strife affect his sleep) and that after the winter passes and spring begins he'll find someone that he can let his heart love.

The whole pestilence, plague, and city clears lines are curious to me because no one mentions them. There is clearly a reference beyond connecting pestilence as a word to the plague that eats flesh, but I haven't encountered or have forgotten the literary reference comparing non-requited love to disease. It's probably middle ages-y like Chaucer or Boccaccio because the choice of the words pestilence and plague and describing good times as the city clearing evoke the bubonic plague, but that's not set in stone.

The 'cheating on a significant other" confusion is founded upon the word shame mostly. But someone cheating won't tell their heart to love their mistress or whatever, that's a function of the heart not receiving enough. Unless you interpret the chorus as the narrator encouraging their heart to love their SO and their heart failing to, which is a big stretch, the lyrics just don't fit that interpretation.