No spells /active/, but spells prepped and slots available?
Disadvantage on /attacks/ only?
That's going to more heavily disfavor some classes than others. Of the Basic 4, the Fighter and Cleric are hosed by lack of armor, especially if they're heavy-armor types - they could be AC 10. The thief, OTOH, loses a little AC, and the wizard is out his Mage Armor, but it's one action to put it up (if he has it prepped - alternately, Shield is a reaction).
Aside from Mage Armor, spells don't often get pre-cast in 5e like they did in 3e, so that's not a huge difference.
For offense, the wizard and cleric can use cantrips or actual spells. The fighter is seriously out of luck, but you said 'big weapons' so the thief may have a dagger and can still SA.
Then there's the disadvantage - bad for the Fighter and Thief and cantrips that take attack rolls, not an issue for spells that force saves or work automatically.