Cornwall is lovely this time of the year but I’d agree with Tang that Devon would be a better choice if riding is the main consideration.
I’m biased but if you’re not too bothered about being on the coast then Eastern Dartmoor would be my recommendation – 30 mins down the A30 to Exeter area (cinemas, Crealy etc), and similar distance to Torbay for organised “fun” stuff if that’s your thing. Under an hour from either North Cornwall or South Devon Coasts for beaches. Lots of nice villages and places to eat in the area, most of which are generally very family friendly.
Moretonhampstead, Chagford and Bovey Tracey all have nice outdoor pools which will be opening in the next couple of weeks too, weather permitting. Pony Centre is nearby and good fun for little ‘uns.
It’s great for kids generally. Lots of rivers to splash in, woods to explore and rock tors to clamber on and terrific riding from the door. Our 4 year old loves it.
Can you tell I like it here? 🙂
All of these have good riding from the door – first one is a good choice for kids (play area, swimming pool, animals etc), and only a couple of miles from the Nutcracker / Cleave:
http://www.helpfulholidays.com/property.asp?ref=A137&year=2014
http://www.helpfulholidays.com/property.asp?ref=A15&year=2014
http://www.helpfulholidays.com/property.asp?ref=A111&year=2014
http://www.helpfulholidays.com/property.asp?ref=A106&year=2014