Both islands are excellent suggestions, good winter sites. Duck, White Tailed Eagles and redpolls, Crossbills and maybe a bonus bird such as Pine Grosbeak...
Weather will be most likely snow and arund minus ten to fifteen degrees, though not windy, so if you wrap up you should be fine. good warm clothes and boots are a must though.
Hjällstaviken is another good inland winter site. Best to play it by ear and see what is around at the time. Often birds can stay in the same area in January. Also depends on whether certain species have erupted south, ie,Owls, Pine Grosbeak etc.
Angarn often a good bet. Sandemar has White tailed Eagle in January, though can be rather devoid of birds at times. Smew will be present.
With regard to duck a hard freeze will mean ice over all inland sites and birds moving to open water on the achipelaga. Stocckholm Strom in the city centre can then hold a lot of birds as it always has open water....