Why does everyone think that small firms automatically means layoffs? 😐 Some firms I'm sure aren't good at workforce management and intentionally overhire and then layoff, but others hire who they need and keep who they get (and then replace those who leave to go elsewhere). A good way to know which one you're in would be by finding out what they've done historically. Do you hear about mass layoffs after busy season previously? If so, then after busy season, you may be in trouble. If not, then you're probably fine.
This time of year there's not too much work to be doing, so could be that everyone else is working on things like organizing records from last year and sorting out their email inbox, which of course you don't have since you weren't there last year. So, I wouldn't take downtime in your first month of being hired as a bad sign – they wouldn't have hired you 2 weeks ago if they were going to not need you 2 weeks later. However, if you've got downtime in May and they have a history of layoffs after busy season, then maybe worry.
The other thing to keep in mind is that people are always more hesitant to lay off good employees than bad ones. That's not to say that good employees don't get laid off, cause the practicalities of financial situations at times require the layoffs of even the best employees. However, if they hire 50 new employees and after busy season can only keep 2 of those, you can rest assured they'll keep the 2 best. Or if after busy season they didn't plan to keep any, but you were a really really good employee, they'll try to see if there's a way they can keep you on before letting you go. So, if the firm's having financial troubles they'll let you go before they cut their own salaries, cause that's just the way life is most of the time. However, if they're able to keep anyone, you can do a lot to make it more likely that you're one of the ones they keep.
And…there's a decent chance that they'll be keeping most if not all of you anyway. My prior paragraph was just a “worse case scenario” type thing. 🙂