If you are wanting to milk your cows over winter, then unless your ground just doesn't get muddy, you will want them housed over winter. The problem with keeping them out with access to a shelter is that the ground around the shelter quickly becomes a quagmire, it's hard then to get to it to bed them, and they can start to sink into the mud and get mud on the teats, leading to mastitis. (Even if they are not in milk over winter, getting mud on the teats is a recipe for mastitis after calving... ask me how I know :/)
Jerseys need a *lot* of grass, so if you do go for cattle, I'd recommend something less high performance, for instance like the Shetland or Northern Dairy Shorthorn (not to be confused with a regular Dairy Shorthorn). They won't produce as much milk as a Jersey but they will manage on significantly less grass, and worse grass, than a Jersey, and generally be easier to keep well.
Which do you prefer, goats or cows? Keeping milking animals is a *lot* of work, and has to be done every day in all weathers, so it's a good idea to choose animals you really like!