Islam teaches that public displays of affection between opposite sexes (meaning married people in this case - segregation is assumed otherwise) is a no-no,
because as people you don't want to evoke feelings of jealousy or what have you, from others. Not everyone is happily married or married at all.
I was out shopping with my husband last night, in the souks near Farwaniya - he held my hand for most of the time.
But, it's discreet..and when walking where we have to go near men or go around, he'll let go and I'll walk around them - as little contact as posisble with non-mehram, or men I cannot marry (meaning family) is a way of life here for most of the women.
The gulf road area, around Salmiya...you might find that you're pretty comfortable there - lots of "western" shops and restaurants in that area and the behavior might be more lax in that sense too - I don't know, for me because I live in a Bedouin town, on the other side of Kuwait (nearer to Ahmadi), I find the atmosphere there to be a lot different.
I find the men in the gulf road area to be astonishingly rude, ill-mannered...perhaps though that is because I know how they are raised and what values/morals they have overall as a society...and the gulf area is where the "bad muslims" tend to hang out, sadly.
The atmosphere and acceptability of social practices changes as you head towards Fahaheel and Ahmadi -
my husband doesn't tend to hold my hand in his hometown, for example. It's more conservative. It takes some getting used to, but again, as foreigners they don't expect you to act like they do - just be more discreet when in those areas and you'll be fine.
Anything western - particularily women - amongst some of the arab men here (the non-practicing ones, and more of the young-ish ones), is something quite yummy and it means "non protected" and up for grabs, pretty much, if the opportunity arises.
Oh, also, when you're driving - whether it's you or her -
she might not want to look out the window, to the side I mean - even looking back before making a turn to change lanes, any eye contact can be seen as a sign of encouragement - and she doesn't want to be followed home by some eager admirer 
(I learned this the hard way lol) . Also smiles and the like are taken in an entirely different way here - that's flirting here. Not mere politeness, the way westerners usually mean it.